(X+1)(x-5)=15

Solution for (X+1)(x-5)=15 equation:

(X+1)(X-5)=15

We move all terms to the left:

(X+1)(X-5)-(15)=0

We multiply parentheses ..

(+X^2-5X+X-5)-15=0

We get rid of parentheses

X^2-5X+X-5-15=0

We add all the numbers together, and all the variables

X^2-4X-20=0

a = 1; b = -4; c = -20;
Δ = b2-4ac
Δ = -42-4·1·(-20)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{6}}{2*1}=\frac{4-4\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{6}}{2*1}=\frac{4+4\sqrt{6}}{2}
$