3/y=7y

Solution for 3/y=7y equation:

3/y=7y

We move all terms to the left:

3/y-(7y)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-7y+3/y=0

We multiply all the terms by the denominator


-7y*y+3=0

Wy multiply elements

-7y^2+3=0

a = -7; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-7)·3
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*-7}=\frac{0-2\sqrt{21}}{-14}
=-\frac{2\sqrt{21}}{-14}
=-\frac{\sqrt{21}}{-7}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*-7}=\frac{0+2\sqrt{21}}{-14}
=\frac{2\sqrt{21}}{-14}
=\frac{\sqrt{21}}{-7}
$