6/x+5=3x+2/x

Solution for 6/x+5=3x+2/x equation:

6/x+5=3x+2/x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

6/x-3x-2/x+5=0

We multiply all the terms by the denominator


-3x*x+5*x+6-2=0

We add all the numbers together, and all the variables

5x-3x*x+4=0

Wy multiply elements

-3x^2+5x+4=0

a = -3; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·(-3)·4
Δ = 73
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{73}}{2*-3}=\frac{-5-\sqrt{73}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*-3}=\frac{-5+\sqrt{73}}{-6}
$