2y+1/y+4=1

Solution for 2y+1/y+4=1 equation:

2y+1/y+4=1

We move all terms to the left:

2y+1/y+4-(1)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

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