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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-4x^2+4x-x+2=0

We add all the numbers together, and all the variables

-4x^2+3x+2=0

a = -4; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-4)·2
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{41}}{2*-4}=\frac{-3-\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*-4}=\frac{-3+\sqrt{41}}{-8}
$