96x+16x^2=24

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

96x+16x^2=24

We move all terms to the left:

96x+16x^2-(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}
$