Solve for p y=3p^2-4

$y = 3 p^{2} - 4$

Step 1

Rewrite the equation as $3 p^{2} - 4 = y$ .

$3 p^{2} - 4 = y$

Step 2

Add $4$ to both sides of the equation.

$3 p^{2} = y + 4$

Step 3

Divide each term in $3 p^{2} = y + 4$ by $3$ and simplify.

Divide each term in $3 p^{2} = y + 4$ by $3$ .

$\frac{3 p^{2}}{3} = \frac{y}{3} + \frac{4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 p^{2}}{3} = \frac{y}{3} + \frac{4}{3}$

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

$p^{2} = \frac{y}{3} + \frac{4}{3}$

Step 4

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

$p = \pm \sqrt{\frac{y}{3} + \frac{4}{3}}$

Step 5

Simplify $\pm \sqrt{\frac{y}{3} + \frac{4}{3}}$ .

Combine the numerators over the common denominator.

$p = \pm \sqrt{\frac{y + 4}{3}}$

Rewrite $\sqrt{\frac{y + 4}{3}}$ as $\frac{\sqrt{y + 4}}{\sqrt{3}}$ .

$p = \pm \frac{\sqrt{y + 4}}{\sqrt{3}}$

Multiply $\frac{\sqrt{y + 4}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$p = \pm \frac{\sqrt{y + 4}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{y + 4}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

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

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{{\sqrt{3}}^{2}}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

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

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

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

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{3^{\frac{2}{2}}}$

Rewrite the expression.

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{3^{1}}$

Evaluate the exponent.

$p = \pm \frac{\sqrt{y + 4} \sqrt{3}}{3}$

Combine using the product rule for radicals.

$p = \pm \frac{\sqrt{(y + 4) \cdot 3}}{3}$

Reorder factors in $\pm \frac{\sqrt{(y + 4) \cdot 3}}{3}$ .

$p = \pm \frac{\sqrt{3 (y + 4)}}{3}$

Step 6

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.

$p = \frac{\sqrt{3 (y + 4)}}{3}$

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

$p = - \frac{\sqrt{3 (y + 4)}}{3}$

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

$p = \frac{\sqrt{3 (y + 4)}}{3}$

$p = - \frac{\sqrt{3 (y + 4)}}{3}$

$p = \frac{\sqrt{3 (y + 4)}}{3}$

$p = - \frac{\sqrt{3 (y + 4)}}{3}$

Solve for p y=3p^2-4

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