Solve Using the Quadratic Formula -6x^2+x-6=-8x^2

$- 6 x^{2} + x - 6 = - 8 x^{2}$

Step 1

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

Add $8 x^{2}$ to both sides of the equation.

$- 6 x^{2} + x - 6 + 8 x^{2} = 0$

Add $- 6 x^{2}$ and $8 x^{2}$ .

$2 x^{2} + x - 6 = 0$

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 $a = 2$ , $b = 1$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (2 \cdot - 6)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 2 \cdot - 6}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 6$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 1 \pm \sqrt{1 - 8 \cdot - 6}}{2 \cdot 2}$

Multiply $- 8$ by $- 6$ .

$x = \frac{- 1 \pm \sqrt{1 + 48}}{2 \cdot 2}$

Add $1$ and $48$ .

$x = \frac{- 1 \pm \sqrt{49}}{2 \cdot 2}$

Rewrite $49$ as $7^{2}$ .

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

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

$x = \frac{- 1 \pm 7}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 1 \pm 7}{4}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{3}{2}, - 2$