1/5y=100y=

Solution for 1/5y=100y= equation:

1/5y=100y=

We move all terms to the left:

1/5y-(100y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-100y+1/5y=0

We multiply all the terms by the denominator


-100y*5y+1=0

Wy multiply elements

-500y^2+1=0

a = -500; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-500)·1
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*-500}=\frac{0-20\sqrt{5}}{-1000}
=-\frac{20\sqrt{5}}{-1000}
=-\frac{\sqrt{5}}{-50}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*-500}=\frac{0+20\sqrt{5}}{-1000}
=\frac{20\sqrt{5}}{-1000}
=\frac{\sqrt{5}}{-50}
$