2x+3/x+1/x-6=0

Solution for 2x+3/x+1/x-6=0 equation:

2x+3/x+1/x-6=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-6*x+3+1=0

We add all the numbers together, and all the variables

-6x+2x*x+4=0

Wy multiply elements

2x^2-6x+4=0

a = 2; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·2·4
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*2}=\frac{8}{4}
=2
$