2x+3/x=6

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

2x+3/x=6

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2-6x+3=0

a = 2; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·2·3
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*2}=\frac{6-2\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*2}=\frac{6+2\sqrt{3}}{4}
$