6x(x+7)-20=6x

Solution for 6x(x+7)-20=6x equation:

6x(x+7)-20=6x

We move all terms to the left:

6x(x+7)-20-(6x)=0

We add all the numbers together, and all the variables

-6x+6x(x+7)-20=0

We multiply parentheses

6x^2-6x+42x-20=0

We add all the numbers together, and all the variables

6x^2+36x-20=0

a = 6; b = 36; c = -20;
Δ = b2-4ac
Δ = 362-4·6·(-20)
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{111}}{2*6}=\frac{-36-4\sqrt{111}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{111}}{2*6}=\frac{-36+4\sqrt{111}}{12}
$