C(X)=(x)(2400x+7)-(20x^2+7x+3500)

Solution for C(X)=(x)(2400x+7)-(20x^2+7x+3500) equation:

(C)=(C)(2400C+7)-(20C^2+7C+3500)

We move all terms to the left:

(C)-((C)(2400C+7)-(20C^2+7C+3500))=0


We calculate terms in parentheses: -(C(2400C+7)-(20C^2+7C+3500)), so:

C(2400C+7)-(20C^2+7C+3500)

We multiply parentheses

2400C^2+7C-(20C^2+7C+3500)

We get rid of parentheses

2400C^2-20C^2+7C-7C-3500

We add all the numbers together, and all the variables

2380C^2-3500

Back to the equation:

-(2380C^2-3500)


We get rid of parentheses

-2380C^2+C+3500=0

a = -2380; b = 1; c = +3500;
Δ = b2-4ac
Δ = 12-4·(-2380)·3500
Δ = 33320001
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{-(1)-\sqrt{33320001}}{2*-2380}=\frac{-1-\sqrt{33320001}}{-4760}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33320001}}{2*-2380}=\frac{-1+\sqrt{33320001}}{-4760}
$