9y/7-9+2=5y/y-9

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

9y/7-9+2=5y/y-9

We move all terms to the left:

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


Domain of the equation: y-9)!=0

y∈R


We add all the numbers together, and all the variables

9y/7-(5y/y-9)-7=0

We get rid of parentheses

9y/7-5y/y+9-7=0

We calculate fractions


9y^2/7y+(-35y)/7y+9-7=0

We add all the numbers together, and all the variables

9y^2/7y+(-35y)/7y+2=0

We multiply all the terms by the denominator


9y^2+(-35y)+2*7y=0

Wy multiply elements

9y^2+(-35y)+14y=0

We get rid of parentheses

9y^2-35y+14y=0

We add all the numbers together, and all the variables

9y^2-21y=0

a = 9; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·9·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*9}=\frac{0}{18}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*9}=\frac{42}{18}
=2+1/3
$