C(x)=x^2+80x+900I(x)=50x

Solution for C(x)=x^2+80x+900I(x)=50x equation:

(C)=C^2+80C+900(C)=50C

We move all terms to the left:

(C)-(C^2+80C+900(C))=0

We get rid of parentheses

-C^2+C-80C-900C=0

We add all the numbers together, and all the variables

-1C^2-979C=0

a = -1; b = -979; c = 0;
Δ = b2-4ac
Δ = -9792-4·(-1)·0
Δ = 958441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{958441}=979$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-979)-979}{2*-1}=\frac{0}{-2}
=0
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-979)+979}{2*-1}=\frac{1958}{-2}
=-979
$