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

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

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

We move all terms to the left:

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


Domain of the equation: x-1)!=0

x∈R


We add all the numbers together, and all the variables

2x-(6/x-1)+1=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x+2x*x-6=0

Wy multiply elements

2x^2+2x-6=0

a = 2; b = 2; c = -6;
Δ = b2-4ac
Δ = 22-4·2·(-6)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{13}}{2*2}=\frac{-2-2\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{13}}{2*2}=\frac{-2+2\sqrt{13}}{4}
$