(x+2)*(x-3)=100

Solution for (x+2)*(x-3)=100 equation:

(x+2)(x-3)=100

We move all terms to the left:

(x+2)(x-3)-(100)=0

We multiply parentheses ..

(+x^2-3x+2x-6)-100=0

We get rid of parentheses

x^2-3x+2x-6-100=0

We add all the numbers together, and all the variables

x^2-1x-106=0

a = 1; b = -1; c = -106;
Δ = b2-4ac
Δ = -12-4·1·(-106)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{17}}{2*1}=\frac{1-5\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{17}}{2*1}=\frac{1+5\sqrt{17}}{2}
$