6(x^2-x-2)=24

Solution for 6(x^2-x-2)=24 equation:

6(x^2-x-2)=24

We move all terms to the left:

6(x^2-x-2)-(24)=0

We multiply parentheses

6x^2-6x-12-24=0

We add all the numbers together, and all the variables

6x^2-6x-36=0

a = 6; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·6·(-36)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*6}=\frac{36}{12}
=3
$