6y+11=10/y

Solution for 6y+11=10/y equation:

6y+11=10/y

We move all terms to the left:

6y+11-(10/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

6y-(+10/y)+11=0

We get rid of parentheses

6y-10/y+11=0

We multiply all the terms by the denominator


6y*y+11*y-10=0

We add all the numbers together, and all the variables

11y+6y*y-10=0

Wy multiply elements

6y^2+11y-10=0

a = 6; b = 11; c = -10;
Δ = b2-4ac
Δ = 112-4·6·(-10)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*6}=\frac{-30}{12}
=-2+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*6}=\frac{8}{12}
=2/3
$