3/y=y/8y-45

Solution for 3/y=y/8y-45 equation:

3/y=y/8y-45

We move all terms to the left:

3/y-(y/8y-45)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 8y-45)!=0

y∈R


We get rid of parentheses

3/y-y/8y+45=0

We calculate fractions


(-1y^2)/8y^2+24y/8y^2+45=0

We multiply all the terms by the denominator


(-1y^2)+24y+45*8y^2=0

Wy multiply elements

(-1y^2)+360y^2+24y=0

We get rid of parentheses

-1y^2+360y^2+24y=0

We add all the numbers together, and all the variables

359y^2+24y=0

a = 359; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·359·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*359}=\frac{-48}{718}
=-24/359
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*359}=\frac{0}{718}
=0
$