150=-16x^2+128x+6

Solution for 150=-16x^2+128x+6 equation:

150=-16x^2+128x+6

We move all terms to the left:

150-(-16x^2+128x+6)=0

We get rid of parentheses

16x^2-128x-6+150=0

We add all the numbers together, and all the variables

16x^2-128x+144=0

a = 16; b = -128; c = +144;
Δ = b2-4ac
Δ = -1282-4·16·144
Δ = 7168
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:

$\sqrt{\Delta}=\sqrt{7168}=\sqrt{1024*7}=\sqrt{1024}*\sqrt{7}=32\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-32\sqrt{7}}{2*16}=\frac{128-32\sqrt{7}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+32\sqrt{7}}{2*16}=\frac{128+32\sqrt{7}}{32}
$