(x-3)(x+6)=9x-18

Solution for (x-3)(x+6)=9x-18 equation:

(x-3)(x+6)=9x-18

We move all terms to the left:

(x-3)(x+6)-(9x-18)=0

We get rid of parentheses

(x-3)(x+6)-9x+18=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-6x=0

a = 1; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·1·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*1}=\frac{12}{2}
=6
$