5/6y+1=-1/3y=8/9

Solution for 5/6y+1=-1/3y=8/9 equation:

5/6y+1=-1/3y=8/9

We move all terms to the left:

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


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We get rid of parentheses

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

We calculate fractions


15y/18y^2+6y/18y^2+1=0

We multiply all the terms by the denominator


15y+6y+1*18y^2=0

We add all the numbers together, and all the variables

21y+1*18y^2=0

Wy multiply elements

18y^2+21y=0

a = 18; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·18·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*18}=\frac{-42}{36}
=-1+1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*18}=\frac{0}{36}
=0
$