5/6x-2=-1/x-+1

Solution for 5/6x-2=-1/x-+1 equation:

5/6x-2=-1/x-+1

We move all terms to the left:

5/6x-2-(-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 add all the numbers together, and all the variables

5/6x-(-1/x)-2=0

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

11x-2*6x^2=0

Wy multiply elements

-12x^2+11x=0

a = -12; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-12)·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*-12}=\frac{-22}{-24}
=11/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-12}=\frac{0}{-24}
=0
$