3x(x-6)+12=3x-5

Solution for 3x(x-6)+12=3x-5 equation:

3x(x-6)+12=3x-5

We move all terms to the left:

3x(x-6)+12-(3x-5)=0

We multiply parentheses

3x^2-18x-(3x-5)+12=0

We get rid of parentheses

3x^2-18x-3x+5+12=0

We add all the numbers together, and all the variables

3x^2-21x+17=0

a = 3; b = -21; c = +17;
Δ = b2-4ac
Δ = -212-4·3·17
Δ = 237
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{-(-21)-\sqrt{237}}{2*3}=\frac{21-\sqrt{237}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{237}}{2*3}=\frac{21+\sqrt{237}}{6}
$