Y=2y+1/y+3

Solution for Y=2y+1/y+3 equation:

=2Y+1/Y+3

We move all terms to the left:

-(2Y+1/Y+3)=0


Domain of the equation: Y+3)!=0

Y∈R


We get rid of parentheses

-2Y-1/Y-3=0

We multiply all the terms by the denominator


-2Y*Y-3*Y-1=0

We add all the numbers together, and all the variables

-3Y-2Y*Y-1=0

Wy multiply elements

-2Y^2-3Y-1=0

a = -2; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·(-2)·(-1)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-1}{2*-2}=\frac{2}{-4}
=-1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+1}{2*-2}=\frac{4}{-4}
=-1
$