4x(x-2)=-1

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

4x(x-2)=-1

We move all terms to the left:

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

We add all the numbers together, and all the variables

4x(x-2)+1=0

We multiply parentheses

4x^2-8x+1=0

a = 4; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·4·1
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{3}}{2*4}=\frac{8-4\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{3}}{2*4}=\frac{8+4\sqrt{3}}{8}
$