(x-7)(x+5)=7

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

(x-7)(x+5)=7

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-2x-42=0

a = 1; b = -2; c = -42;
Δ = b2-4ac
Δ = -22-4·1·(-42)
Δ = 172
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{43}}{2*1}=\frac{2-2\sqrt{43}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{43}}{2*1}=\frac{2+2\sqrt{43}}{2}
$