-16x^2+20x=5

Solution for -16x^2+20x=5 equation:

-16x^2+20x=5

We move all terms to the left:

-16x^2+20x-(5)=0

a = -16; b = 20; c = -5;
Δ = b2-4ac
Δ = 202-4·(-16)·(-5)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{5}}{2*-16}=\frac{-20-4\sqrt{5}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{5}}{2*-16}=\frac{-20+4\sqrt{5}}{-32}
$