15y-1=(11)/(2y)+2

Solution for 15y-1=(11)/(2y)+2 equation:

15y-1=(11)/(2y)+2

We move all terms to the left:

15y-1-((11)/(2y)+2)=0


Domain of the equation: 2y+2)!=0

y∈R


We get rid of parentheses

15y-11/2y-2-1=0

We multiply all the terms by the denominator


15y*2y-2*2y-1*2y-11=0

Wy multiply elements

30y^2-4y-2y-11=0

We add all the numbers together, and all the variables

30y^2-6y-11=0

a = 30; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·30·(-11)
Δ = 1356
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:

$\sqrt{\Delta}=\sqrt{1356}=\sqrt{4*339}=\sqrt{4}*\sqrt{339}=2\sqrt{339}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{339}}{2*30}=\frac{6-2\sqrt{339}}{60}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{339}}{2*30}=\frac{6+2\sqrt{339}}{60}
$