2/4x+2=x

Solution for 2/4x+2=x equation:

2/4x+2=x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+2/4x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -4; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·(-4)·2
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*-4}=\frac{-8-4\sqrt{6}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*-4}=\frac{-8+4\sqrt{6}}{-8}
$