24=96x+16x^2

Solution for 24=96x+16x^2 equation:

24=96x+16x^2

We move all terms to the left:

24-(96x+16x^2)=0

We get rid of parentheses

-16x^2-96x+24=0

a = -16; b = -96; c = +24;
Δ = b2-4ac
Δ = -962-4·(-16)·24
Δ = 10752
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10752}=\sqrt{256*42}=\sqrt{256}*\sqrt{42}=16\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16\sqrt{42}}{2*-16}=\frac{96-16\sqrt{42}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16\sqrt{42}}{2*-16}=\frac{96+16\sqrt{42}}{-32}
$