(4(2-x))/(3+x)=x

Solution for (4(2-x))/(3+x)=x equation:

(4(2-x))/(3+x)=x

We move all terms to the left:

(4(2-x))/(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

(4(-1x+2))/(x+3)-x=0

We add all the numbers together, and all the variables

-1x+(4(-1x+2))/(x+3)=0

We multiply all the terms by the denominator


-1x*(x+3)+(4(-1x+2))=0


We calculate terms in parentheses: +(4(-1x+2)), so:

4(-1x+2)

We multiply parentheses

-4x+8

Back to the equation:

+(-4x+8)


We multiply parentheses

-x^2-3x+(-4x+8)=0

We get rid of parentheses

-x^2-3x-4x+8=0

We add all the numbers together, and all the variables

-1x^2-7x+8=0

a = -1; b = -7; c = +8;
Δ = b2-4ac
Δ = -72-4·(-1)·8
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*-1}=\frac{16}{-2}
=-8
$