C(x)=3x^2+15x+C(x)=3x^2+15x+75

Solution for C(x)=3x^2+15x+C(x)=3x^2+15x+75 equation:

(C)=3C^2+15C+(C)=3C^2+15C+75

We move all terms to the left:

(C)-(3C^2+15C+(C))=0

We get rid of parentheses

-3C^2+C-15C-C=0

We add all the numbers together, and all the variables

-3C^2-15C=0

a = -3; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-3)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-3}=\frac{0}{-6}
=0
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-3}=\frac{30}{-6}
=-5
$