x+4/x=3x/x+2

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

x+4/x=3x/x+2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-5x+x*x+4=0

Wy multiply elements

x^2-5x+4=0

a = 1; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·1·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*1}=\frac{8}{2}
=4
$