(X-12)(x+10)=85

Solution for (X-12)(x+10)=85 equation:

(X-12)(X+10)=85

We move all terms to the left:

(X-12)(X+10)-(85)=0

We multiply parentheses ..

(+X^2+10X-12X-120)-85=0

We get rid of parentheses

X^2+10X-12X-120-85=0

We add all the numbers together, and all the variables

X^2-2X-205=0

a = 1; b = -2; c = -205;
Δ = b2-4ac
Δ = -22-4·1·(-205)
Δ = 824
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:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{206}}{2*1}=\frac{2-2\sqrt{206}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{206}}{2*1}=\frac{2+2\sqrt{206}}{2}
$