7/9y-3/7y=-1

Solution for 7/9y-3/7y=-1 equation:

7/9y-3/7y=-1

We move all terms to the left:

7/9y-3/7y-(-1)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R



Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We add all the numbers together, and all the variables

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

We calculate fractions


49y/63y^2+(-27y)/63y^2+1=0

We multiply all the terms by the denominator


49y+(-27y)+1*63y^2=0

Wy multiply elements

63y^2+49y+(-27y)=0

We get rid of parentheses

63y^2+49y-27y=0

We add all the numbers together, and all the variables

63y^2+22y=0

a = 63; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·63·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*63}=\frac{-44}{126}
=-22/63
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*63}=\frac{0}{126}
=0
$