3/y=y/5y-18

Solution for 3/y=y/5y-18 equation:

3/y=y/5y-18

We move all terms to the left:

3/y-(y/5y-18)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 5y-18)!=0

y∈R


We get rid of parentheses

3/y-y/5y+18=0

We calculate fractions


(-1y^2)/5y^2+15y/5y^2+18=0

We multiply all the terms by the denominator


(-1y^2)+15y+18*5y^2=0

Wy multiply elements

(-1y^2)+90y^2+15y=0

We get rid of parentheses

-1y^2+90y^2+15y=0

We add all the numbers together, and all the variables

89y^2+15y=0

a = 89; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·89·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*89}=\frac{-30}{178}
=-15/89
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*89}=\frac{0}{178}
=0
$