(X+3)(x-2)=8

Solution for (X+3)(x-2)=8 equation:

(X+3)(X-2)=8

We move all terms to the left:

(X+3)(X-2)-(8)=0

We multiply parentheses ..

(+X^2-2X+3X-6)-8=0

We get rid of parentheses

X^2-2X+3X-6-8=0

We add all the numbers together, and all the variables

X^2+X-14=0

a = 1; b = 1; c = -14;
Δ = b2-4ac
Δ = 12-4·1·(-14)
Δ = 57
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{57}}{2*1}=\frac{-1-\sqrt{57}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*1}=\frac{-1+\sqrt{57}}{2}
$