(11+5*x)/(3+x)=x

Solution for (11+5*x)/(3+x)=x equation:

(11+5x)/(3+x)=x

We move all terms to the left:

(11+5x)/(3+x)-(x)=0


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

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

x!=-3

x∈R


We add all the numbers together, and all the variables

(5x+11)/(x+3)-x=0

We add all the numbers together, and all the variables

-1x+(5x+11)/(x+3)=0

We multiply all the terms by the denominator


-1x*(x+3)+(5x+11)=0

We multiply parentheses

-x^2-3x+(5x+11)=0

We get rid of parentheses

-x^2-3x+5x+11=0

We add all the numbers together, and all the variables

-1x^2+2x+11=0

a = -1; b = 2; c = +11;
Δ = b2-4ac
Δ = 22-4·(-1)·11
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{3}}{2*-1}=\frac{-2-4\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{3}}{2*-1}=\frac{-2+4\sqrt{3}}{-2}
$