108=-16x^2+96x

Solution for 108=-16x^2+96x equation:

108=-16x^2+96x

We move all terms to the left:

108-(-16x^2+96x)=0

We get rid of parentheses

16x^2-96x+108=0

a = 16; b = -96; c = +108;
Δ = b2-4ac
Δ = -962-4·16·108
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-48}{2*16}=\frac{48}{32}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+48}{2*16}=\frac{144}{32}
=4+1/2
$