C=150-50x+x^2

Solution for C=150-50x+x^2 equation:

=150-50C+C^2

We move all terms to the left:

-(150-50C+C^2)=0

We get rid of parentheses

-C^2+50C-150=0

We add all the numbers together, and all the variables

-1C^2+50C-150=0

a = -1; b = 50; c = -150;
Δ = b2-4ac
Δ = 502-4·(-1)·(-150)
Δ = 1900
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:

$\sqrt{\Delta}=\sqrt{1900}=\sqrt{100*19}=\sqrt{100}*\sqrt{19}=10\sqrt{19}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{19}}{2*-1}=\frac{-50-10\sqrt{19}}{-2}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{19}}{2*-1}=\frac{-50+10\sqrt{19}}{-2}
$