4/(2-x)+x=4

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

4/(2-x)+x=4

We move all terms to the left:

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


Domain of the equation: (2-x)!=0

We move all terms containing x to the left, all other terms to the right

-x!=-2

x!=-2/-1

x!=+2

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

-1x^2+2x+4x-8+4=0

We add all the numbers together, and all the variables

-1x^2+6x-4=0

a = -1; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·(-1)·(-4)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{5}}{2*-1}=\frac{-6-2\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{5}}{2*-1}=\frac{-6+2\sqrt{5}}{-2}
$