(x+1)(x-7)=84

Solution for (x+1)(x-7)=84 equation:

(x+1)(x-7)=84

We move all terms to the left:

(x+1)(x-7)-(84)=0

We multiply parentheses ..

(+x^2-7x+x-7)-84=0

We get rid of parentheses

x^2-7x+x-7-84=0

We add all the numbers together, and all the variables

x^2-6x-91=0

a = 1; b = -6; c = -91;
Δ = b2-4ac
Δ = -62-4·1·(-91)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-20}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+20}{2*1}=\frac{26}{2}
=13
$