C(x)=0.5x2-170x+25,850

Solution for C(x)=0.5x2-170x+25,850 equation:

(C)=0.5C^2-170C+25.850

We move all terms to the left:

(C)-(0.5C^2-170C+25.850)=0

We get rid of parentheses

-0.5C^2+C+170C-25.850=0

We add all the numbers together, and all the variables

-0.5C^2+171C-25.85=0

a = -0.5; b = 171; c = -25.85;
Δ = b2-4ac
Δ = 1712-4·(-0.5)·(-25.85)
Δ = 29189.3
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(171)-\sqrt{29189.3}}{2*-0.5}=\frac{-171-\sqrt{29189.3}}{-1}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(171)+\sqrt{29189.3}}{2*-0.5}=\frac{-171+\sqrt{29189.3}}{-1}
$