21/(4+2x)=x

Solution for 21/(4+2x)=x equation:

21/(4+2x)=x

We move all terms to the left:

21/(4+2x)-(x)=0


Domain of the equation: (4+2x)!=0

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

2x!=-4

x!=-4/2

x!=-2

x∈R


We add all the numbers together, and all the variables

21/(2x+4)-x=0

We add all the numbers together, and all the variables

-1x+21/(2x+4)=0

We multiply all the terms by the denominator


-1x*(2x+4)+21=0

We multiply parentheses

-2x^2-4x+21=0

a = -2; b = -4; c = +21;
Δ = b2-4ac
Δ = -42-4·(-2)·21
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{46}}{2*-2}=\frac{4-2\sqrt{46}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{46}}{2*-2}=\frac{4+2\sqrt{46}}{-4}
$