(3x-9)(2x-5)=0

Solution for (3x-9)(2x-5)=0 equation:

(3x-9)(2x-5)=0

We multiply parentheses ..

(+6x^2-15x-18x+45)=0

We get rid of parentheses

6x^2-15x-18x+45=0

We add all the numbers together, and all the variables

6x^2-33x+45=0

a = 6; b = -33; c = +45;
Δ = b2-4ac
Δ = -332-4·6·45
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3}{2*6}=\frac{30}{12}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3}{2*6}=\frac{36}{12}
=3
$