3x-6+2(x+6)x+6=36

Solution for 3x-6+2(x+6)x+6=36 equation:

3x-6+2(x+6)x+6=36

We move all terms to the left:

3x-6+2(x+6)x+6-(36)=0

We add all the numbers together, and all the variables

3x+2(x+6)x-36=0

We multiply parentheses

2x^2+3x+12x-36=0

We add all the numbers together, and all the variables

2x^2+15x-36=0

a = 2; b = 15; c = -36;
Δ = b2-4ac
Δ = 152-4·2·(-36)
Δ = 513
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{57}}{2*2}=\frac{-15-3\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{57}}{2*2}=\frac{-15+3\sqrt{57}}{4}
$