21/2y=2y

Solution for 21/2y=2y equation:

21/2y=2y

We move all terms to the left:

21/2y-(2y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-2y+21/2y=0

We multiply all the terms by the denominator


-2y*2y+21=0

Wy multiply elements

-4y^2+21=0

a = -4; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-4)·21
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{21}}{2*-4}=\frac{0-4\sqrt{21}}{-8}
=-\frac{4\sqrt{21}}{-8}
=-\frac{\sqrt{21}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{21}}{2*-4}=\frac{0+4\sqrt{21}}{-8}
=\frac{4\sqrt{21}}{-8}
=\frac{\sqrt{21}}{-2}
$