c*(c+15)=150

Solution for c*(c+15)=150 equation:

c(c+15)=150

We move all terms to the left:

c(c+15)-(150)=0

We multiply parentheses

c^2+15c-150=0

a = 1; b = 15; c = -150;
Δ = b2-4ac
Δ = 152-4·1·(-150)
Δ = 825
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{33}}{2*1}=\frac{-15-5\sqrt{33}}{2}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{33}}{2*1}=\frac{-15+5\sqrt{33}}{2}
$