(x-6)(x+1)=2(x+1)

Solution for (x-6)(x+1)=2(x+1) equation:

(x-6)(x+1)=2(x+1)

We move all terms to the left:

(x-6)(x+1)-(2(x+1))=0

We multiply parentheses ..

(+x^2+x-6x-6)-(2(x+1))=0


We calculate terms in parentheses: -(2(x+1)), so:

2(x+1)

We multiply parentheses

2x+2

Back to the equation:

-(2x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-7x-8=0

a = 1; b = -7; c = -8;
Δ = b2-4ac
Δ = -72-4·1·(-8)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*1}=\frac{16}{2}
=8
$