(x+6)(3x-2)=5x+2x

Solution for (x+6)(3x-2)=5x+2x equation:

(x+6)(3x-2)=5x+2x

We move all terms to the left:

(x+6)(3x-2)-(5x+2x)=0

We add all the numbers together, and all the variables

(x+6)(3x-2)-(+7x)=0

We get rid of parentheses

(x+6)(3x-2)-7x=0

We multiply parentheses ..

(+3x^2-2x+18x-12)-7x=0

We get rid of parentheses

3x^2-2x+18x-7x-12=0

We add all the numbers together, and all the variables

3x^2+9x-12=0

a = 3; b = 9; c = -12;
Δ = b2-4ac
Δ = 92-4·3·(-12)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*3}=\frac{6}{6}
=1
$