Solve for x g(x)=ax^2+24

$g (x) = a x^{2} + 24$

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

$g x - a x^{2} = 24$

Subtract $24$ from both sides of the equation.

$g x - a x^{2} - 24 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = - a$ , $b = g$ , and $c = - 24$ into the quadratic formula and solve for $x$ .

$\frac{- g \pm \sqrt{g^{2} - 4 \cdot (- a \cdot - 24)}}{2 (- a)}$

Simplify.

Simplify the numerator.

Multiply $- 4$ by $- 1$ .

$x = \frac{- g \pm \sqrt{g^{2} + 4 a \cdot - 24}}{2 (- a)}$

Multiply $- 24$ by $4$ .

$x = \frac{- g \pm \sqrt{g^{2} - 96 a}}{2 (- a)}$

Multiply $- 1$ by $2$ .

$x = \frac{- g \pm \sqrt{g^{2} - 96 a}}{- 2 a}$

Simplify $\frac{- g \pm \sqrt{g^{2} - 96 a}}{- 2 a}$ .

$x = \frac{g \pm \sqrt{g^{2} - 96 a}}{2 a}$

The final answer is the combination of both solutions.

$x = \frac{g + \sqrt{g^{2} - 96 a}}{2 a}$

$x = \frac{g - \sqrt{g^{2} - 96 a}}{2 a}$