3x^2-6=9x-6

Solution for 3x^2-6=9x-6 equation:

3x^2-6=9x-6

We move all terms to the left:

3x^2-6-(9x-6)=0

We get rid of parentheses

3x^2-9x+6-6=0

We add all the numbers together, and all the variables

3x^2-9x=0

a = 3; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·3·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*3}=\frac{18}{6}
=3
$