(x-5)(x+7)=12

Solution for (x-5)(x+7)=12 equation:

(x-5)(x+7)=12

We move all terms to the left:

(x-5)(x+7)-(12)=0

We multiply parentheses ..

(+x^2+7x-5x-35)-12=0

We get rid of parentheses

x^2+7x-5x-35-12=0

We add all the numbers together, and all the variables

x^2+2x-47=0

a = 1; b = 2; c = -47;
Δ = b2-4ac
Δ = 22-4·1·(-47)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{3}}{2*1}=\frac{-2-8\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{3}}{2*1}=\frac{-2+8\sqrt{3}}{2}
$