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

Solution for 9x(x-6)-2(x-6)=0 equation:

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

We multiply parentheses

9x^2-54x-2x+12=0

We add all the numbers together, and all the variables

9x^2-56x+12=0

a = 9; b = -56; c = +12;
Δ = b2-4ac
Δ = -562-4·9·12
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-52}{2*9}=\frac{4}{18}
=2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+52}{2*9}=\frac{108}{18}
=6
$