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

Solution for (6x-18)(3x-2)=0 equation:

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

We multiply parentheses ..

(+18x^2-12x-54x+36)=0

We get rid of parentheses

18x^2-12x-54x+36=0

We add all the numbers together, and all the variables

18x^2-66x+36=0

a = 18; b = -66; c = +36;
Δ = b2-4ac
Δ = -662-4·18·36
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-42}{2*18}=\frac{24}{36}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+42}{2*18}=\frac{108}{36}
=3
$