4/5y=30y=

Solution for 4/5y=30y= equation:

4/5y=30y=

We move all terms to the left:

4/5y-(30y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-30y+4/5y=0

We multiply all the terms by the denominator


-30y*5y+4=0

Wy multiply elements

-150y^2+4=0

a = -150; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-150)·4
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*-150}=\frac{0-20\sqrt{6}}{-300}
=-\frac{20\sqrt{6}}{-300}
=-\frac{\sqrt{6}}{-15}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*-150}=\frac{0+20\sqrt{6}}{-300}
=\frac{20\sqrt{6}}{-300}
=\frac{\sqrt{6}}{-15}
$