(9x-27)(3x-4)=0

Solution for (9x-27)(3x-4)=0 equation:

(9x-27)(3x-4)=0

We multiply parentheses ..

(+27x^2-36x-81x+108)=0

We get rid of parentheses

27x^2-36x-81x+108=0

We add all the numbers together, and all the variables

27x^2-117x+108=0

a = 27; b = -117; c = +108;
Δ = b2-4ac
Δ = -1172-4·27·108
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-45}{2*27}=\frac{72}{54}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+45}{2*27}=\frac{162}{54}
=3
$