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^2-8=0

We multiply all the terms by the denominator


10y+6y-8*12y^2=0

We add all the numbers together, and all the variables

16y-8*12y^2=0

Wy multiply elements

-96y^2+16y=0

a = -96; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-96)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-96}=\frac{-32}{-192}
=1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-96}=\frac{0}{-192}
=0
$