c2=150

Solution for c2=150 equation:

c2=150

We move all terms to the left:

c2-(150)=0

We add all the numbers together, and all the variables

c^2-150=0

a = 1; b = 0; c = -150;
Δ = b2-4ac
Δ = 02-4·1·(-150)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*1}=\frac{0-10\sqrt{6}}{2}
=-\frac{10\sqrt{6}}{2}
=-5\sqrt{6}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*1}=\frac{0+10\sqrt{6}}{2}
=\frac{10\sqrt{6}}{2}
=5\sqrt{6}
$