Solve for x 4x^2-30x=12+10x

$4 x^{2} - 30 x = 12 + 10 x$

Move all terms containing $x$ to the left side of the equation.

Subtract $10 x$ from both sides of the equation.

$4 x^{2} - 30 x - 10 x = 12$

Subtract $10 x$ from $- 30 x$ .

$4 x^{2} - 40 x = 12$

Subtract $12$ from both sides of the equation.

$4 x^{2} - 40 x - 12 = 0$

Factor $4$ out of $4 x^{2} - 40 x - 12$ .

Factor $4$ out of $4 x^{2}$ .

$4 (x^{2}) - 40 x - 12 = 0$

Factor $4$ out of $- 40 x$ .

$4 (x^{2}) + 4 (- 10 x) - 12 = 0$

Factor $4$ out of $- 12$ .

$4 x^{2} + 4 (- 10 x) + 4 \cdot - 3 = 0$

Factor $4$ out of $4 x^{2} + 4 (- 10 x)$ .

$4 (x^{2} - 10 x) + 4 \cdot - 3 = 0$

Factor $4$ out of $4 (x^{2} - 10 x) + 4 \cdot - 3$ .

$4 (x^{2} - 10 x - 3) = 0$

Divide each term in $4 (x^{2} - 10 x - 3) = 0$ by $4$ and simplify.

Divide each term in $4 (x^{2} - 10 x - 3) = 0$ by $4$ .

$\frac{4 (x^{2} - 10 x - 3)}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 (x^{2} - 10 x - 3)}{4} = \frac{0}{4}$

Divide $x^{2} - 10 x - 3$ by $1$ .

$x^{2} - 10 x - 3 = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x^{2} - 10 x - 3 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = - 10$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{10 \pm \sqrt{{(- 10)}^{2} - 4 \cdot (1 \cdot - 3)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $- 10$ to the power of $2$ .

$x = \frac{10 \pm \sqrt{100 - 4 \cdot 1 \cdot - 3}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{10 \pm \sqrt{100 - 4 \cdot - 3}}{2 \cdot 1}$

Multiply $- 4$ by $- 3$ .

$x = \frac{10 \pm \sqrt{100 + 12}}{2 \cdot 1}$

Add $100$ and $12$ .

$x = \frac{10 \pm \sqrt{112}}{2 \cdot 1}$

Rewrite $112$ as $4^{2} \cdot 7$ .

Factor $16$ out of $112$ .

$x = \frac{10 \pm \sqrt{16 (7)}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{10 \pm \sqrt{4^{2} \cdot 7}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{10 \pm 4 \sqrt{7}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{10 \pm 4 \sqrt{7}}{2}$

Simplify $\frac{10 \pm 4 \sqrt{7}}{2}$ .

$x = 5 \pm 2 \sqrt{7}$

The final answer is the combination of both solutions.

$x = 5 + 2 \sqrt{7}, 5 - 2 \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$x = 5 + 2 \sqrt{7}, 5 - 2 \sqrt{7}$

Decimal Form:

$x = 10.29150262 \dots, - 0.29150262 \dots$

Solve for x 4x^2-30x=12+10x

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