80=-16x^2+100x

Solution for 80=-16x^2+100x equation:

80=-16x^2+100x

We move all terms to the left:

80-(-16x^2+100x)=0

We get rid of parentheses

16x^2-100x+80=0

a = 16; b = -100; c = +80;
Δ = b2-4ac
Δ = -1002-4·16·80
Δ = 4880
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:

$\sqrt{\Delta}=\sqrt{4880}=\sqrt{16*305}=\sqrt{16}*\sqrt{305}=4\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{305}}{2*16}=\frac{100-4\sqrt{305}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{305}}{2*16}=\frac{100+4\sqrt{305}}{32}
$