-16x^2+80x=60

Solution for -16x^2+80x=60 equation:

-16x^2+80x=60

We move all terms to the left:

-16x^2+80x-(60)=0

a = -16; b = 80; c = -60;
Δ = b2-4ac
Δ = 802-4·(-16)·(-60)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-16\sqrt{10}}{2*-16}=\frac{-80-16\sqrt{10}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+16\sqrt{10}}{2*-16}=\frac{-80+16\sqrt{10}}{-32}
$