2+3/x=4+x

Solution for 2+3/x=4+x equation:

2+3/x=4+x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/x-x-4+2=0

We multiply all the terms by the denominator


-x*x-4*x+2*x+3=0

We add all the numbers together, and all the variables

-2x-x*x+3=0

Wy multiply elements

-1x^2-2x+3=0

a = -1; b = -2; c = +3;
Δ = b2-4ac
Δ = -22-4·(-1)·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*-1}=\frac{6}{-2}
=-3
$