(3x-1)(-2x+3)=0

Solution for (3x-1)(-2x+3)=0 equation:

(3x-1)(-2x+3)=0

We multiply parentheses ..

(-6x^2+9x+2x-3)=0

We get rid of parentheses

-6x^2+9x+2x-3=0

We add all the numbers together, and all the variables

-6x^2+11x-3=0

a = -6; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·(-6)·(-3)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*-6}=\frac{-4}{-12}
=1/3
$