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

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

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

We multiply parentheses ..

(+10x^2-18x-15x+27)=0

We get rid of parentheses

10x^2-18x-15x+27=0

We add all the numbers together, and all the variables

10x^2-33x+27=0

a = 10; b = -33; c = +27;
Δ = b2-4ac
Δ = -332-4·10·27
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*10}=\frac{30}{20}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3}{2*10}=\frac{36}{20}
=1+4/5
$