(x-5)(x-7)=63

Solution for (x-5)(x-7)=63 equation:

(x-5)(x-7)=63

We move all terms to the left:

(x-5)(x-7)-(63)=0

We multiply parentheses ..

(+x^2-7x-5x+35)-63=0

We get rid of parentheses

x^2-7x-5x+35-63=0

We add all the numbers together, and all the variables

x^2-12x-28=0

a = 1; b = -12; c = -28;
Δ = b2-4ac
Δ = -122-4·1·(-28)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16}{2*1}=\frac{28}{2}
=14
$