# How do you solve -8+9x^2+5=-9x^2+5?

Oct 24, 2016

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

#### Explanation:

Solve: $- 8 + 9 {x}^{2} + 5 = - 9 {x}^{2} + 5$

Simplify.

$9 {x}^{2} - 3 = - 9 {x}^{2} + 5$

Add $3$ to both sides.

$9 {x}^{2} = - 9 {x}^{2} + 5 + 3$

Add $9 {x}^{2}$ to both sides.

$9 {x}^{2} + 9 {x}^{2} = 5 + 3$

Simplify.

$18 {x}^{2} = 8$

Subtract $8$ from both sides.

$18 {x}^{2} - 8 = 0$

This is a quadratic equation of the form $a {x}^{2} + b x + c$, where $a = 18$, $b = 0$, $c = - 8$.

The value for $x$ can be determined using the quadratic formula.

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 \cdot a \cdot c}}{2 a}$

$x = \frac{- 0 \pm \sqrt{{0}^{2} - 4 \cdot 18 \cdot - 8}}{2 \cdot 18}$

Simplify.

$x = \frac{\pm \sqrt{576}}{36}$

Simplify.

$x = \pm \frac{24}{36}$

Simplify.

$x = \pm \frac{4}{9}$

Simplify.

$x = \pm \frac{2}{3}$

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