3x=6/x-1

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

3x=6/x-1

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

3x-6/x+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+3x*x-6=0

Wy multiply elements

3x^2+x-6=0

a = 3; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·3·(-6)
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{-(1)-\sqrt{73}}{2*3}=\frac{-1-\sqrt{73}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{73}}{2*3}=\frac{-1+\sqrt{73}}{6}
$