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=0

a = -0.5; b = 171; c = 0;
Δ = b2-4ac
Δ = 1712-4·(-0.5)·0
Δ = 29241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29241}=171$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(171)-171}{2*-0.5}=\frac{-342}{-1}
=+342
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(171)+171}{2*-0.5}=\frac{0}{-1}
=0
$