2x(4x-1)=0

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

2x(4x-1)=0

We multiply parentheses

8x^2-2x=0

a = 8; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·8·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*8}=\frac{4}{16}
=1/4
$