10-1/2y=1/y

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

10-1/2y=1/y

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-y)/2y^2+(-2y)/2y^2+10=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


(-1y)+(-2y)+10*2y^2=0

Wy multiply elements

20y^2+(-1y)+(-2y)=0

We get rid of parentheses

20y^2-1y-2y=0

We add all the numbers together, and all the variables

20y^2-3y=0

a = 20; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·20·0
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*20}=\frac{0}{40}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*20}=\frac{6}{40}
=3/20
$