(x-5)(x-7)=35

Solution for (x-5)(x-7)=35 equation:

(x-5)(x-7)=35

We move all terms to the left:

(x-5)(x-7)-(35)=0

We multiply parentheses ..

(+x^2-7x-5x+35)-35=0

We get rid of parentheses

x^2-7x-5x+35-35=0

We add all the numbers together, and all the variables

x^2-12x=0

a = 1; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·1·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*1}=\frac{24}{2}
=12
$