9(2x-6)(x+3)=4x-18

Solution for 9(2x-6)(x+3)=4x-18 equation:

9(2x-6)(x+3)=4x-18

We move all terms to the left:

9(2x-6)(x+3)-(4x-18)=0

We get rid of parentheses

9(2x-6)(x+3)-4x+18=0

We multiply parentheses ..

9(+2x^2+6x-6x-18)-4x+18=0

We multiply parentheses

18x^2+54x-54x-4x-162+18=0

We add all the numbers together, and all the variables

18x^2-4x-144=0

a = 18; b = -4; c = -144;
Δ = b2-4ac
Δ = -42-4·18·(-144)
Δ = 10384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10384}=\sqrt{16*649}=\sqrt{16}*\sqrt{649}=4\sqrt{649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{649}}{2*18}=\frac{4-4\sqrt{649}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{649}}{2*18}=\frac{4+4\sqrt{649}}{36}
$