2/x=3+x

Solution for 2/x=3+x equation:

2/x=3+x

We move all terms to the left:

2/x-(3+x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2/x-(x+3)=0

We get rid of parentheses

2/x-x-3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-3x-x*x+2=0

Wy multiply elements

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

a = -1; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-1)·2
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{17}}{2*-1}=\frac{3-\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{17}}{2*-1}=\frac{3+\sqrt{17}}{-2}
$