(-2x+1)(3x-5)=0

Solution for (-2x+1)(3x-5)=0 equation:

(-2x+1)(3x-5)=0

We multiply parentheses ..

(-6x^2+10x+3x-5)=0

We get rid of parentheses

-6x^2+10x+3x-5=0

We add all the numbers together, and all the variables

-6x^2+13x-5=0

a = -6; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·(-6)·(-5)
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{-(13)-7}{2*-6}=\frac{-20}{-12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+7}{2*-6}=\frac{-6}{-12}
=1/2
$