6(x-6)-5x(x-7)=x+6

Solution for 6(x-6)-5x(x-7)=x+6 equation:

6(x-6)-5x(x-7)=x+6

We move all terms to the left:

6(x-6)-5x(x-7)-(x+6)=0

We multiply parentheses

-5x^2+6x+35x-(x+6)-36=0

We get rid of parentheses

-5x^2+6x+35x-x-6-36=0

We add all the numbers together, and all the variables

-5x^2+40x-42=0

a = -5; b = 40; c = -42;
Δ = b2-4ac
Δ = 402-4·(-5)·(-42)
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{190}}{2*-5}=\frac{-40-2\sqrt{190}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{190}}{2*-5}=\frac{-40+2\sqrt{190}}{-10}
$