-5/6y-1/9y=-102

Solution for -5/6y-1/9y=-102 equation:

-5/6y-1/9y=-102

We move all terms to the left:

-5/6y-1/9y-(-102)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We add all the numbers together, and all the variables

-5/6y-1/9y+102=0

We calculate fractions


(-45y)/54y^2+(-6y)/54y^2+102=0

We multiply all the terms by the denominator


(-45y)+(-6y)+102*54y^2=0

Wy multiply elements

5508y^2+(-45y)+(-6y)=0

We get rid of parentheses

5508y^2-45y-6y=0

We add all the numbers together, and all the variables

5508y^2-51y=0

a = 5508; b = -51; c = 0;
Δ = b2-4ac
Δ = -512-4·5508·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-51}{2*5508}=\frac{0}{11016}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+51}{2*5508}=\frac{102}{11016}
=1/108
$