(-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{-36}{-20}
=1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3}{2*-10}=\frac{-30}{-20}
=1+1/2
$