(x+1)(x-5)=135

Solution for (x+1)(x-5)=135 equation:

(X+1)(X-5)=135

We move all terms to the left:

(X+1)(X-5)-(135)=0

We multiply parentheses ..

(+X^2-5X+X-5)-135=0

We get rid of parentheses

X^2-5X+X-5-135=0

We add all the numbers together, and all the variables

X^2-4X-140=0

a = 1; b = -4; c = -140;
Δ = b2-4ac
Δ = -42-4·1·(-140)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-24}{2*1}=\frac{-20}{2}
=-10
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+24}{2*1}=\frac{28}{2}
=14
$