C=10000-110x+.045x^2

Solution for C=10000-110x+.045x^2 equation:

=10000-110C+.045C^2

We move all terms to the left:

-(10000-110C+.045C^2)=0

We get rid of parentheses

-.045C^2+110C-10000=0

We add all the numbers together, and all the variables

-0.045C^2+110C-10000=0

a = -0.045; b = 110; c = -10000;
Δ = b2-4ac
Δ = 1102-4·(-0.045)·(-10000)
Δ = 10300
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:

$\sqrt{\Delta}=\sqrt{10300}=\sqrt{100*103}=\sqrt{100}*\sqrt{103}=10\sqrt{103}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-10\sqrt{103}}{2*-0.045}=\frac{-110-10\sqrt{103}}{-0.09}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+10\sqrt{103}}{2*-0.045}=\frac{-110+10\sqrt{103}}{-0.09}
$