(2x-1)(-4x+3)=0

Solution for (2x-1)(-4x+3)=0 equation:

(2x-1)(-4x+3)=0

We multiply parentheses ..

(-8x^2+6x+4x-3)=0

We get rid of parentheses

-8x^2+6x+4x-3=0

We add all the numbers together, and all the variables

-8x^2+10x-3=0

a = -8; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·(-8)·(-3)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*-8}=\frac{-12}{-16}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*-8}=\frac{-8}{-16}
=1/2
$