(1/2y+10)+4=-1/y+5

Solution for (1/2y+10)+4=-1/y+5 equation:

(1/2y+10)+4=-1/y+5

We move all terms to the left:

(1/2y+10)+4-(-1/y+5)=0


Domain of the equation: 2y+10)!=0

y∈R



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

y∈R


We get rid of parentheses

1/2y+1/y+10-5+4=0

We calculate fractions


y/2y^2+2y/2y^2+10-5+4=0

We add all the numbers together, and all the variables

y/2y^2+2y/2y^2+9=0

We multiply all the terms by the denominator


y+2y+9*2y^2=0

We add all the numbers together, and all the variables

3y+9*2y^2=0

Wy multiply elements

18y^2+3y=0

a = 18; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·18·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*18}=\frac{-6}{36}
=-1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*18}=\frac{0}{36}
=0
$