13/18y+1=-6/16y

Solution for 13/18y+1=-6/16y equation:

13/18y+1=-6/16y

We move all terms to the left:

13/18y+1-(-6/16y)=0


Domain of the equation: 18y!=0

y!=0/18

y!=0

y∈R



Domain of the equation: 16y)!=0

y!=0/1

y!=0

y∈R


We get rid of parentheses

13/18y+6/16y+1=0

We calculate fractions


208y/288y^2+108y/288y^2+1=0

We multiply all the terms by the denominator


208y+108y+1*288y^2=0

We add all the numbers together, and all the variables

316y+1*288y^2=0

Wy multiply elements

288y^2+316y=0

a = 288; b = 316; c = 0;
Δ = b2-4ac
Δ = 3162-4·288·0
Δ = 99856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{99856}=316$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(316)-316}{2*288}=\frac{-632}{576}
=-1+7/72
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(316)+316}{2*288}=\frac{0}{576}
=0
$