1/2y+10+1=-2/y+5

Solution for 1/2y+10+1=-2/y+5 equation:

1/2y+10+1=-2/y+5

We move all terms to the left:

1/2y+10+1-(-2/y+5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y+5)!=0

y∈R


We add all the numbers together, and all the variables

1/2y-(-2/y+5)+11=0

We get rid of parentheses

1/2y+2/y-5+11=0

We calculate fractions


y/2y^2+4y/2y^2-5+11=0

We add all the numbers together, and all the variables

y/2y^2+4y/2y^2+6=0

We multiply all the terms by the denominator


y+4y+6*2y^2=0

We add all the numbers together, and all the variables

5y+6*2y^2=0

Wy multiply elements

12y^2+5y=0

a = 12; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·12·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*12}=\frac{-10}{24}
=-5/12
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*12}=\frac{0}{24}
=0
$