150=-16x^2+128x

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

150=-16x^2+128x

We move all terms to the left:

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

We get rid of parentheses

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}
$