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

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

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

We move all terms to the left:

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

We multiply parentheses

3x^2-18x-(5x-6)+6=0

We get rid of parentheses

3x^2-18x-5x+6+6=0

We add all the numbers together, and all the variables

3x^2-23x+12=0

a = 3; b = -23; c = +12;
Δ = b2-4ac
Δ = -232-4·3·12
Δ = 385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{385}}{2*3}=\frac{23-\sqrt{385}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{385}}{2*3}=\frac{23+\sqrt{385}}{6}
$