y-6/y=19/y

Solution for y-6/y=19/y equation:

y-6/y=19/y

We move all terms to the left:

y-6/y-(19/y)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-6/y-(+19/y)=0

We get rid of parentheses

y-6/y-19/y=0

We multiply all the terms by the denominator


y*y-6-19=0

We add all the numbers together, and all the variables

y*y-25=0

Wy multiply elements

y^2-25=0

a = 1; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·1·(-25)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*1}=\frac{-10}{2}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*1}=\frac{10}{2}
=5
$