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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

X^2-5X+7X-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}
$