2x+3/x=5

Solution for 2x+3/x=5 equation:

2x+3/x=5

We move all terms to the left:

2x+3/x-(5)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-5*x+3=0

We add all the numbers together, and all the variables

-5x+2x*x+3=0

Wy multiply elements

2x^2-5x+3=0

a = 2; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·2·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*2}=\frac{6}{4}
=1+1/2
$