C=(25-x)(x-7)

Solution for C=(25-x)(x-7) equation:

=(25-C)(C-7)

We move all terms to the left:

-((25-C)(C-7))=0

We add all the numbers together, and all the variables

-((-1C+25)(C-7))=0

We multiply parentheses ..

-((-1C^2+7C+25C-175))=0


We calculate terms in parentheses: -((-1C^2+7C+25C-175)), so:

(-1C^2+7C+25C-175)

We get rid of parentheses

-1C^2+7C+25C-175

We add all the numbers together, and all the variables

-1C^2+32C-175

Back to the equation:

-(-1C^2+32C-175)


We get rid of parentheses

1C^2-32C+175=0

We add all the numbers together, and all the variables

C^2-32C+175=0

a = 1; b = -32; c = +175;
Δ = b2-4ac
Δ = -322-4·1·175
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-18}{2*1}=\frac{14}{2}
=7
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+18}{2*1}=\frac{50}{2}
=25
$