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

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

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

We multiply parentheses ..

(-15x^2+5x+6x-2)=0

We get rid of parentheses

-15x^2+5x+6x-2=0

We add all the numbers together, and all the variables

-15x^2+11x-2=0

a = -15; b = 11; c = -2;
Δ = b2-4ac
Δ = 112-4·(-15)·(-2)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-1}{2*-15}=\frac{-12}{-30}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+1}{2*-15}=\frac{-10}{-30}
=1/3
$