Solve for d Fd^2+3=t^3

$F d^{2} + 3 = t^{3}$

Subtract $3$ from both sides of the equation.

$F d^{2} = t^{3} - 3$

Divide each term in $F d^{2} = t^{3} - 3$ by $F$ and simplify.

Divide each term in $F d^{2} = t^{3} - 3$ by $F$ .

$\frac{F d^{2}}{F} = \frac{t^{3}}{F} + \frac{- 3}{F}$

Simplify the left side.

Cancel the common factor of $F$ .

Cancel the common factor.

$\frac{F d^{2}}{F} = \frac{t^{3}}{F} + \frac{- 3}{F}$

Divide $d^{2}$ by $1$ .

$d^{2} = \frac{t^{3}}{F} + \frac{- 3}{F}$

Simplify the right side.

Move the negative in front of the fraction.

$d^{2} = \frac{t^{3}}{F} - \frac{3}{F}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$d = \pm \sqrt{\frac{t^{3}}{F} - \frac{3}{F}}$

Simplify $\pm \sqrt{\frac{t^{3}}{F} - \frac{3}{F}}$ .

Combine the numerators over the common denominator.

$d = \pm \sqrt{\frac{t^{3} - 3}{F}}$

Rewrite $\sqrt{\frac{t^{3} - 3}{F}}$ as $\frac{\sqrt{t^{3} - 3}}{\sqrt{F}}$ .

$d = \pm \frac{\sqrt{t^{3} - 3}}{\sqrt{F}}$

Multiply $\frac{\sqrt{t^{3} - 3}}{\sqrt{F}}$ by $\frac{\sqrt{F}}{\sqrt{F}}$ .

$d = \pm \frac{\sqrt{t^{3} - 3}}{\sqrt{F}} \cdot \frac{\sqrt{F}}{\sqrt{F}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{t^{3} - 3}}{\sqrt{F}}$ by $\frac{\sqrt{F}}{\sqrt{F}}$ .

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{\sqrt{F} \sqrt{F}}$

Raise $\sqrt{F}$ to the power of $1$ .

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{{\sqrt{F}}^{1} \sqrt{F}}$

Raise $\sqrt{F}$ to the power of $1$ .

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{{\sqrt{F}}^{1} {\sqrt{F}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{{\sqrt{F}}^{1 + 1}}$

Add $1$ and $1$ .

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{{\sqrt{F}}^{2}}$

Rewrite ${\sqrt{F}}^{2}$ as $F$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{F}$ as $F^{\frac{1}{2}}$ .

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{{(F^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{F^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{F^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{F^{\frac{2}{2}}}$

Rewrite the expression.

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{F^{1}}$

Simplify.

$d = \pm \frac{\sqrt{t^{3} - 3} \sqrt{F}}{F}$

Combine using the product rule for radicals.

$d = \pm \frac{\sqrt{(t^{3} - 3) F}}{F}$

Reorder factors in $\pm \frac{\sqrt{(t^{3} - 3) F}}{F}$ .

$d = \pm \frac{\sqrt{F (t^{3} - 3)}}{F}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$d = \frac{\sqrt{F (t^{3} - 3)}}{F}$

Next, use the negative value of the $\pm$ to find the second solution.

$d = - \frac{\sqrt{F (t^{3} - 3)}}{F}$

The complete solution is the result of both the positive and negative portions of the solution.

$d = \frac{\sqrt{F (t^{3} - 3)}}{F}$

$d = - \frac{\sqrt{F (t^{3} - 3)}}{F}$

$d = \frac{\sqrt{F (t^{3} - 3)}}{F}$

$d = - \frac{\sqrt{F (t^{3} - 3)}}{F}$

Solve for d Fd^2+3=t^3

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