3x+1/x=5

Solution for 3x+1/x=5 equation:

3x+1/x=5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-5x+1=0

a = 3; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·3·1
Δ = 13
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{-(-5)-\sqrt{13}}{2*3}=\frac{5-\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*3}=\frac{5+\sqrt{13}}{6}
$