5/6x-3=-1/x+1

Solution for 5/6x-3=-1/x+1 equation:

5/6x-3=-1/x+1

We move all terms to the left:

5/6x-3-(-1/x+1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/6x+1/x-1-3=0

We calculate fractions


5x/6x^2+6x/6x^2-1-3=0

We add all the numbers together, and all the variables

5x/6x^2+6x/6x^2-4=0

We multiply all the terms by the denominator


5x+6x-4*6x^2=0

We add all the numbers together, and all the variables

11x-4*6x^2=0

Wy multiply elements

-24x^2+11x=0

a = -24; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-24)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-24}=\frac{-22}{-48}
=11/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-24}=\frac{0}{-48}
=0
$