5y=5/9y

Solution for 5y=5/9y equation:

5y=5/9y

We move all terms to the left:

5y-(5/9y)=0


Domain of the equation: 9y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5y-5/9y=0

We multiply all the terms by the denominator


5y*9y-5=0

Wy multiply elements

45y^2-5=0

a = 45; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·45·(-5)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*45}=\frac{-30}{90}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*45}=\frac{30}{90}
=1/3
$