9x-18=3x^2-6x

Solution for 9x-18=3x^2-6x equation:

9x-18=3x^2-6x

We move all terms to the left:

9x-18-(3x^2-6x)=0

We get rid of parentheses

-3x^2+9x+6x-18=0

We add all the numbers together, and all the variables

-3x^2+15x-18=0

a = -3; b = 15; c = -18;
Δ = b2-4ac
Δ = 152-4·(-3)·(-18)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3}{2*-3}=\frac{-12}{-6}
=+2
$