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

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

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

We multiply parentheses ..

(-10x^2+15x+6x-9)=0

We get rid of parentheses

-10x^2+15x+6x-9=0

We add all the numbers together, and all the variables

-10x^2+21x-9=0

a = -10; b = 21; c = -9;
Δ = b2-4ac
Δ = 212-4·(-10)·(-9)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-9}{2*-10}=\frac{-30}{-20}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+9}{2*-10}=\frac{-12}{-20}
=3/5
$