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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

8x^2+2x-4x-1-2=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
$