5/6y=5y=

Solution for 5/6y=5y= equation:

5/6y=5y=

We move all terms to the left:

5/6y-(5y)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

-5y+5/6y=0

We multiply all the terms by the denominator


-5y*6y+5=0

Wy multiply elements

-30y^2+5=0

a = -30; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-30)·5
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*-30}=\frac{0-10\sqrt{6}}{-60}
=-\frac{10\sqrt{6}}{-60}
=-\frac{\sqrt{6}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*-30}=\frac{0+10\sqrt{6}}{-60}
=\frac{10\sqrt{6}}{-60}
=\frac{\sqrt{6}}{-6}
$