(-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^2-2x+3=0

a = -8; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-8)·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-8}=\frac{-8}{-16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-8}=\frac{12}{-16}
=-3/4
$