13/6y-5/2y+13/18=7/9

Solution for 13/6y-5/2y+13/18=7/9 equation:

13/6y-5/2y+13/18=7/9

We move all terms to the left:

13/6y-5/2y+13/18-(7/9)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

13/6y-5/2y+13/18-(+7/9)=0

We get rid of parentheses

13/6y-5/2y+13/18-7/9=0

We calculate fractions


(-3024y^2)/1944y^2+2808y^2/1944y^2+4212y/1944y^2+(-4860y)/1944y^2=0

We multiply all the terms by the denominator


(-3024y^2)+2808y^2+4212y+(-4860y)=0

We add all the numbers together, and all the variables

2808y^2+(-3024y^2)+4212y+(-4860y)=0

We get rid of parentheses

2808y^2-3024y^2+4212y-4860y=0

We add all the numbers together, and all the variables

-216y^2-648y=0

a = -216; b = -648; c = 0;
Δ = b2-4ac
Δ = -6482-4·(-216)·0
Δ = 419904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{419904}=648$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-648)-648}{2*-216}=\frac{0}{-432}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-648)+648}{2*-216}=\frac{1296}{-432}
=-3
$