4/9y+1/6y=3/7

Solution for 4/9y+1/6y=3/7 equation:

4/9y+1/6y=3/7

We move all terms to the left:

4/9y+1/6y-(3/7)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

4/9y+1/6y-(+3/7)=0

We get rid of parentheses

4/9y+1/6y-3/7=0

We calculate fractions


(-972y^2)/2646y^2+1176y/2646y^2+441y/2646y^2=0

We multiply all the terms by the denominator


(-972y^2)+1176y+441y=0

We add all the numbers together, and all the variables

(-972y^2)+1617y=0

We get rid of parentheses

-972y^2+1617y=0

a = -972; b = 1617; c = 0;
Δ = b2-4ac
Δ = 16172-4·(-972)·0
Δ = 2614689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2614689}=1617$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1617)-1617}{2*-972}=\frac{-3234}{-1944}
=1+215/324
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1617)+1617}{2*-972}=\frac{0}{-1944}
=0
$