C(x)=4x^2-384x+46

Solution for C(x)=4x^2-384x+46 equation:

(C)=4C^2-384C+46

We move all terms to the left:

(C)-(4C^2-384C+46)=0

We get rid of parentheses

-4C^2+C+384C-46=0

We add all the numbers together, and all the variables

-4C^2+385C-46=0

a = -4; b = 385; c = -46;
Δ = b2-4ac
Δ = 3852-4·(-4)·(-46)
Δ = 147489
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{-(385)-\sqrt{147489}}{2*-4}=\frac{-385-\sqrt{147489}}{-8}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(385)+\sqrt{147489}}{2*-4}=\frac{-385+\sqrt{147489}}{-8}
$