2/y+9/2y=-13/4

Solution for 2/y+9/2y=-13/4 equation:

2/y+9/2y=-13/4

We move all terms to the left:

2/y+9/2y-(-13/4)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

2/y+9/2y+13/4=0

We calculate fractions


52y^2/32y^2+64y/32y^2+144y/32y^2=0

We multiply all the terms by the denominator


52y^2+64y+144y=0

We add all the numbers together, and all the variables

52y^2+208y=0

a = 52; b = 208; c = 0;
Δ = b2-4ac
Δ = 2082-4·52·0
Δ = 43264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43264}=208$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-208}{2*52}=\frac{-416}{104}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+208}{2*52}=\frac{0}{104}
=0
$