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

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

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

We move all terms to the left:

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

We multiply parentheses

2x^2+x+8x-(4x-2)=0

We get rid of parentheses

2x^2+x+8x-4x+2=0

We add all the numbers together, and all the variables

2x^2+5x+2=0

a = 2; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·2·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*2}=\frac{-2}{4}
=-1/2
$