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