Solve Using the Quadratic Formula 15x^2-56=88+6x^2

$15 x^{2} - 56 = 88 + 6 x^{2}$

Step 1

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Subtract $88$ from both sides of the equation.

$15 x^{2} - 56 - 88 = 6 x^{2}$

Subtract $6 x^{2}$ from both sides of the equation.

$15 x^{2} - 56 - 88 - 6 x^{2} = 0$

Simplify $15 x^{2} - 56 - 88 - 6 x^{2}$ .

Subtract $6 x^{2}$ from $15 x^{2}$ .

$9 x^{2} - 56 - 88 = 0$

Subtract $88$ from $- 56$ .

$9 x^{2} - 144 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 9$ , $b = 0$ , and $c = - 144$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (9 \cdot - 144)}}{2 \cdot 9}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 9 \cdot - 144}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot - 144$ .

Multiply $- 4$ by $9$ .

$x = \frac{0 \pm \sqrt{0 - 36 \cdot - 144}}{2 \cdot 9}$

Multiply $- 36$ by $- 144$ .

$x = \frac{0 \pm \sqrt{0 + 5184}}{2 \cdot 9}$

Add $0$ and $5184$ .

$x = \frac{0 \pm \sqrt{5184}}{2 \cdot 9}$

Rewrite $5184$ as $72^{2}$ .

$x = \frac{0 \pm \sqrt{72^{2}}}{2 \cdot 9}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm 72}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{0 \pm 72}{18}$

Simplify $\frac{0 \pm 72}{18}$ .

$x = \pm 4$

Step 5

The final answer is the combination of both solutions.

$x = 4, - 4$