20/(2+3x)=x

Solution for 20/(2+3x)=x equation:

20/(2+3x)=x

We move all terms to the left:

20/(2+3x)-(x)=0


Domain of the equation: (2+3x)!=0

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

3x!=-2

x!=-2/3

x!=-2/3

x∈R


We add all the numbers together, and all the variables

20/(3x+2)-x=0

We add all the numbers together, and all the variables

-1x+20/(3x+2)=0

We multiply all the terms by the denominator


-1x*(3x+2)+20=0

We multiply parentheses

-3x^2-2x+20=0

a = -3; b = -2; c = +20;
Δ = b2-4ac
Δ = -22-4·(-3)·20
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{61}}{2*-3}=\frac{2-2\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{61}}{2*-3}=\frac{2+2\sqrt{61}}{-6}
$