(2x-1)(-4x+6)=0

Solution for (2x-1)(-4x+6)=0 equation:

(2x-1)(-4x+6)=0

We multiply parentheses ..

(-8x^2+12x+4x-6)=0

We get rid of parentheses

-8x^2+12x+4x-6=0

We add all the numbers together, and all the variables

-8x^2+16x-6=0

a = -8; b = 16; c = -6;
Δ = b2-4ac
Δ = 162-4·(-8)·(-6)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8}{2*-8}=\frac{-24}{-16}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8}{2*-8}=\frac{-8}{-16}
=1/2
$