-3/2y=5/y-5

Solution for -3/2y=5/y-5 equation:

-3/2y=5/y-5

We move all terms to the left:

-3/2y-(5/y-5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y-5)!=0

y∈R


We get rid of parentheses

-3/2y-5/y+5=0

We calculate fractions


(-3y)/2y^2+(-10y)/2y^2+5=0

We multiply all the terms by the denominator


(-3y)+(-10y)+5*2y^2=0

Wy multiply elements

10y^2+(-3y)+(-10y)=0

We get rid of parentheses

10y^2-3y-10y=0

We add all the numbers together, and all the variables

10y^2-13y=0

a = 10; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·10·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*10}=\frac{0}{20}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*10}=\frac{26}{20}
=1+3/10
$