9/2y+5/y=-1

Solution for 9/2y+5/y=-1 equation:

9/2y+5/y=-1

We move all terms to the left:

9/2y+5/y-(-1)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

9/2y+5/y+1=0

We calculate fractions


9y/2y^2+10y/2y^2+1=0

We multiply all the terms by the denominator


9y+10y+1*2y^2=0

We add all the numbers together, and all the variables

19y+1*2y^2=0

Wy multiply elements

2y^2+19y=0

a = 2; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·2·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*2}=\frac{-38}{4}
=-9+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*2}=\frac{0}{4}
=0
$