(2x+1)(4x-8)=0

Solution for (2x+1)(4x-8)=0 equation:

(2x+1)(4x-8)=0

We multiply parentheses ..

(+8x^2-16x+4x-8)=0

We get rid of parentheses

8x^2-16x+4x-8=0

We add all the numbers together, and all the variables

8x^2-12x-8=0

a = 8; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·8·(-8)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20}{2*8}=\frac{-8}{16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20}{2*8}=\frac{32}{16}
=2
$