(4x-1)(-5x+2)=0

Solution for (4x-1)(-5x+2)=0 equation:

(4x-1)(-5x+2)=0

We multiply parentheses ..

(-20x^2+8x+5x-2)=0

We get rid of parentheses

-20x^2+8x+5x-2=0

We add all the numbers together, and all the variables

-20x^2+13x-2=0

a = -20; b = 13; c = -2;
Δ = b2-4ac
Δ = 132-4·(-20)·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3}{2*-20}=\frac{-16}{-40}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3}{2*-20}=\frac{-10}{-40}
=1/4
$