(x-3)(x+2)=86

Solution for (x-3)(x+2)=86 equation:

(x-3)(x+2)=86

We move all terms to the left:

(x-3)(x+2)-(86)=0

We multiply parentheses ..

(+x^2+2x-3x-6)-86=0

We get rid of parentheses

x^2+2x-3x-6-86=0

We add all the numbers together, and all the variables

x^2-1x-92=0

a = 1; b = -1; c = -92;
Δ = b2-4ac
Δ = -12-4·1·(-92)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{41}}{2*1}=\frac{1-3\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{41}}{2*1}=\frac{1+3\sqrt{41}}{2}
$