11y-2=y+9/y=3/5

Solution for 11y-2=y+9/y=3/5 equation:

11y-2=y+9/y=3/5

We move all terms to the left:

11y-2-(y+9/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

11y-(+y+9/y)-2=0

We get rid of parentheses

11y-y-9/y-2=0

We multiply all the terms by the denominator


11y*y-y*y-2*y-9=0

We add all the numbers together, and all the variables

-2y+11y*y-y*y-9=0

Wy multiply elements

11y^2-1y^2-2y-9=0

We add all the numbers together, and all the variables

10y^2-2y-9=0

a = 10; b = -2; c = -9;
Δ = b2-4ac
Δ = -22-4·10·(-9)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{91}}{2*10}=\frac{2-2\sqrt{91}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{91}}{2*10}=\frac{2+2\sqrt{91}}{20}
$