-16x^2+128x=220

Solution for -16x^2+128x=220 equation:

-16x^2+128x=220

We move all terms to the left:

-16x^2+128x-(220)=0

a = -16; b = 128; c = -220;
Δ = b2-4ac
Δ = 1282-4·(-16)·(-220)
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{-(128)-48}{2*-16}=\frac{-176}{-32}
=5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+48}{2*-16}=\frac{-80}{-32}
=2+1/2
$