5/y=69y=

Solution for 5/y=69y= equation:

5/y=69y=

We move all terms to the left:

5/y-(69y)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-69y+5/y=0

We multiply all the terms by the denominator


-69y*y+5=0

Wy multiply elements

-69y^2+5=0

a = -69; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-69)·5
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{345}}{2*-69}=\frac{0-2\sqrt{345}}{-138}
=-\frac{2\sqrt{345}}{-138}
=-\frac{\sqrt{345}}{-69}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{345}}{2*-69}=\frac{0+2\sqrt{345}}{-138}
=\frac{2\sqrt{345}}{-138}
=\frac{\sqrt{345}}{-69}
$