2x-9/3=6-3/x

Solution for 2x-9/3=6-3/x equation:

2x-9/3=6-3/x

We move all terms to the left:

2x-9/3-(6-3/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(-3/x+6)-9/3=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-9x+2x*x+3=0

Wy multiply elements

2x^2-9x+3=0

a = 2; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·2·3
Δ = 57
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{-(-9)-\sqrt{57}}{2*2}=\frac{9-\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*2}=\frac{9+\sqrt{57}}{4}
$