(3x-27)(2x-1)=0

Solution for (3x-27)(2x-1)=0 equation:

(3x-27)(2x-1)=0

We multiply parentheses ..

(+6x^2-3x-54x+27)=0

We get rid of parentheses

6x^2-3x-54x+27=0

We add all the numbers together, and all the variables

6x^2-57x+27=0

a = 6; b = -57; c = +27;
Δ = b2-4ac
Δ = -572-4·6·27
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-51}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+51}{2*6}=\frac{108}{12}
=9
$