1-2/6y=3/13y

Solution for 1-2/6y=3/13y equation:

1-2/6y=3/13y

We move all terms to the left:

1-2/6y-(3/13y)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 13y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-2/6y-(+3/13y)+1=0

We get rid of parentheses

-2/6y-3/13y+1=0

We calculate fractions


(-26y)/78y^2+(-18y)/78y^2+1=0

We multiply all the terms by the denominator


(-26y)+(-18y)+1*78y^2=0

Wy multiply elements

78y^2+(-26y)+(-18y)=0

We get rid of parentheses

78y^2-26y-18y=0

We add all the numbers together, and all the variables

78y^2-44y=0

a = 78; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·78·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*78}=\frac{0}{156}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*78}=\frac{88}{156}
=22/39
$