(x+2)(x-3)-180=0

Solution for (x+2)(x-3)-180=0 equation:

(x+2)(x-3)-180=0

We multiply parentheses ..

(+x^2-3x+2x-6)-180=0

We get rid of parentheses

x^2-3x+2x-6-180=0

We add all the numbers together, and all the variables

x^2-1x-186=0

a = 1; b = -1; c = -186;
Δ = b2-4ac
Δ = -12-4·1·(-186)
Δ = 745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{745}}{2*1}=\frac{1-\sqrt{745}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{745}}{2*1}=\frac{1+\sqrt{745}}{2}
$