5/9y=25y=

Solution for 5/9y=25y= equation:

5/9y=25y=

We move all terms to the left:

5/9y-(25y)=0


Domain of the equation: 9y!=0

y!=0/9

y!=0

y∈R


We add all the numbers together, and all the variables

-25y+5/9y=0

We multiply all the terms by the denominator


-25y*9y+5=0

Wy multiply elements

-225y^2+5=0

a = -225; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-225)·5
Δ = 4500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{5}}{2*-225}=\frac{0-30\sqrt{5}}{-450}
=-\frac{30\sqrt{5}}{-450}
=-\frac{\sqrt{5}}{-15}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{5}}{2*-225}=\frac{0+30\sqrt{5}}{-450}
=\frac{30\sqrt{5}}{-450}
=\frac{\sqrt{5}}{-15}
$