108=6(x-2)(x+1)

Solution for 108=6(x-2)(x+1) equation:

108=6(x-2)(x+1)

We move all terms to the left:

108-(6(x-2)(x+1))=0

We multiply parentheses ..

-(6(+x^2+x-2x-2))+108=0


We calculate terms in parentheses: -(6(+x^2+x-2x-2)), so:

6(+x^2+x-2x-2)

We multiply parentheses

6x^2+6x-12x-12

We add all the numbers together, and all the variables

6x^2-6x-12

Back to the equation:

-(6x^2-6x-12)


We get rid of parentheses

-6x^2+6x+12+108=0

We add all the numbers together, and all the variables

-6x^2+6x+120=0

a = -6; b = 6; c = +120;
Δ = b2-4ac
Δ = 62-4·(-6)·120
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-54}{2*-6}=\frac{-60}{-12}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+54}{2*-6}=\frac{48}{-12}
=-4
$