80=96+80x-16x^2

Solution for 80=96+80x-16x^2 equation:

80=96+80x-16x^2

We move all terms to the left:

80-(96+80x-16x^2)=0

We get rid of parentheses

16x^2-80x-96+80=0

We add all the numbers together, and all the variables

16x^2-80x-16=0

a = 16; b = -80; c = -16;
Δ = b2-4ac
Δ = -802-4·16·(-16)
Δ = 7424
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:

$\sqrt{\Delta}=\sqrt{7424}=\sqrt{256*29}=\sqrt{256}*\sqrt{29}=16\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16\sqrt{29}}{2*16}=\frac{80-16\sqrt{29}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16\sqrt{29}}{2*16}=\frac{80+16\sqrt{29}}{32}
$