3x-1/x+2+2x-1/x+4=3

Solution for 3x-1/x+2+2x-1/x+4=3 equation:

3x-1/x+2+2x-1/x+4=3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-1/x-1/x+3=0

We multiply all the terms by the denominator


5x*x+3*x-1-1=0

We add all the numbers together, and all the variables

3x+5x*x-2=0

Wy multiply elements

5x^2+3x-2=0

a = 5; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·5·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-7}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*5}=\frac{4}{10}
=2/5
$