5/6y+1=1/2y-9

Solution for 5/6y+1=1/2y-9 equation:

5/6y+1=1/2y-9

We move all terms to the left:

5/6y+1-(1/2y-9)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 2y-9)!=0

y∈R


We get rid of parentheses

5/6y-1/2y+9+1=0

We calculate fractions


10y/12y^2+(-6y)/12y^2+9+1=0

We add all the numbers together, and all the variables

10y/12y^2+(-6y)/12y^2+10=0

We multiply all the terms by the denominator


10y+(-6y)+10*12y^2=0

Wy multiply elements

120y^2+10y+(-6y)=0

We get rid of parentheses

120y^2+10y-6y=0

We add all the numbers together, and all the variables

120y^2+4y=0

a = 120; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·120·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*120}=\frac{-8}{240}
=-1/30
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*120}=\frac{0}{240}
=0
$