x^2=8x+150

Solution for x^2=8x+150 equation:

x^2=8x+150

We move all terms to the left:

x^2-(8x+150)=0

We get rid of parentheses

x^2-8x-150=0

a = 1; b = -8; c = -150;
Δ = b2-4ac
Δ = -82-4·1·(-150)
Δ = 664
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:

$\sqrt{\Delta}=\sqrt{664}=\sqrt{4*166}=\sqrt{4}*\sqrt{166}=2\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{166}}{2*1}=\frac{8-2\sqrt{166}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{166}}{2*1}=\frac{8+2\sqrt{166}}{2}
$