C(x)=4x^2-296x+77

Solution for C(x)=4x^2-296x+77 equation:

(C)=4C^2-296C+77

We move all terms to the left:

(C)-(4C^2-296C+77)=0

We get rid of parentheses

-4C^2+C+296C-77=0

We add all the numbers together, and all the variables

-4C^2+297C-77=0

a = -4; b = 297; c = -77;
Δ = b2-4ac
Δ = 2972-4·(-4)·(-77)
Δ = 86977
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{-(297)-\sqrt{86977}}{2*-4}=\frac{-297-\sqrt{86977}}{-8}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(297)+\sqrt{86977}}{2*-4}=\frac{-297+\sqrt{86977}}{-8}
$