-16x^2+128x=150

Solution for -16x^2+128x=150 equation:

-16x^2+128x=150

We move all terms to the left:

-16x^2+128x-(150)=0

a = -16; b = 128; c = -150;
Δ = b2-4ac
Δ = 1282-4·(-16)·(-150)
Δ = 6784
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:

$\sqrt{\Delta}=\sqrt{6784}=\sqrt{64*106}=\sqrt{64}*\sqrt{106}=8\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-8\sqrt{106}}{2*-16}=\frac{-128-8\sqrt{106}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+8\sqrt{106}}{2*-16}=\frac{-128+8\sqrt{106}}{-32}
$