x^2-x-6=3x^2+6x

Solution for x^2-x-6=3x^2+6x equation:

x^2-x-6=3x^2+6x

We move all terms to the left:

x^2-x-6-(3x^2+6x)=0

We add all the numbers together, and all the variables

x^2-1x-(3x^2+6x)-6=0

We get rid of parentheses

x^2-3x^2-1x-6x-6=0

We add all the numbers together, and all the variables

-2x^2-7x-6=0

a = -2; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·(-2)·(-6)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*-2}=\frac{6}{-4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*-2}=\frac{8}{-4}
=-2
$