5/6y+1=1/3y-2

Solution for 5/6y+1=1/3y-2 equation:

5/6y+1=1/3y-2

We move all terms to the left:

5/6y+1-(1/3y-2)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 3y-2)!=0

y∈R


We get rid of parentheses

5/6y-1/3y+2+1=0

We calculate fractions


15y/18y^2+(-6y)/18y^2+2+1=0

We add all the numbers together, and all the variables

15y/18y^2+(-6y)/18y^2+3=0

We multiply all the terms by the denominator


15y+(-6y)+3*18y^2=0

Wy multiply elements

54y^2+15y+(-6y)=0

We get rid of parentheses

54y^2+15y-6y=0

We add all the numbers together, and all the variables

54y^2+9y=0

a = 54; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·54·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*54}=\frac{-18}{108}
=-1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*54}=\frac{0}{108}
=0
$