C-(7-c)(c=5)

Solution for C-(7-c)(c=5) equation:

-(7-C)(C=5)

We move all terms to the left:

-(7-C)(C-(5))=0

We add all the numbers together, and all the variables

-(-1C+7)(C-5)=0

We multiply parentheses ..

-(-1C^2+5C+7C-35)=0

We get rid of parentheses

1C^2-5C-7C+35=0

We add all the numbers together, and all the variables

C^2-12C+35=0

a = 1; b = -12; c = +35;
Δ = b2-4ac
Δ = -122-4·1·35
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2}{2*1}=\frac{10}{2}
=5
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2}{2*1}=\frac{14}{2}
=7
$