(x+5)(x-7)=3

Solution for (x+5)(x-7)=3 equation:

(x+5)(x-7)=3

We move all terms to the left:

(x+5)(x-7)-(3)=0

We multiply parentheses ..

(+x^2-7x+5x-35)-3=0

We get rid of parentheses

x^2-7x+5x-35-3=0

We add all the numbers together, and all the variables

x^2-2x-38=0

a = 1; b = -2; c = -38;
Δ = b2-4ac
Δ = -22-4·1·(-38)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{39}}{2*1}=\frac{2-2\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{39}}{2*1}=\frac{2+2\sqrt{39}}{2}
$