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

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

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

We multiply parentheses ..

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

We multiply parentheses

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

We add all the numbers together, and all the variables

8x^2+6x-2=0

a = 8; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·8·(-2)
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{-(6)-10}{2*8}=\frac{-16}{16}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*8}=\frac{4}{16}
=1/4
$