150=x^2+15x+15

Solution for 150=x^2+15x+15 equation:

150=x^2+15x+15

We move all terms to the left:

150-(x^2+15x+15)=0

We get rid of parentheses

-x^2-15x-15+150=0

We add all the numbers together, and all the variables

-1x^2-15x+135=0

a = -1; b = -15; c = +135;
Δ = b2-4ac
Δ = -152-4·(-1)·135
Δ = 765
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:

$\sqrt{\Delta}=\sqrt{765}=\sqrt{9*85}=\sqrt{9}*\sqrt{85}=3\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{85}}{2*-1}=\frac{15-3\sqrt{85}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{85}}{2*-1}=\frac{15+3\sqrt{85}}{-2}
$