84/y=2y

Solution for 84/y=2y equation:

84/y=2y

We move all terms to the left:

84/y-(2y)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-2y+84/y=0

We multiply all the terms by the denominator


-2y*y+84=0

Wy multiply elements

-2y^2+84=0

a = -2; b = 0; c = +84;
Δ = b2-4ac
Δ = 02-4·(-2)·84
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*-2}=\frac{0-4\sqrt{42}}{-4}
=-\frac{4\sqrt{42}}{-4}
=-\frac{\sqrt{42}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*-2}=\frac{0+4\sqrt{42}}{-4}
=\frac{4\sqrt{42}}{-4}
=\frac{\sqrt{42}}{-1}
$