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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-10x^2+15x+4x-6)=0

We get rid of parentheses

-10x^2+15x+4x-6=0

We add all the numbers together, and all the variables

-10x^2+19x-6=0

a = -10; b = 19; c = -6;
Δ = b2-4ac
Δ = 192-4·(-10)·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-11}{2*-10}=\frac{-30}{-20}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+11}{2*-10}=\frac{-8}{-20}
=2/5
$