1/2y-3=1/10y

Solution for 1/2y-3=1/10y equation:

1/2y-3=1/10y

We move all terms to the left:

1/2y-3-(1/10y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 10y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y-(+1/10y)-3=0

We get rid of parentheses

1/2y-1/10y-3=0

We calculate fractions


10y/20y^2+(-2y)/20y^2-3=0

We multiply all the terms by the denominator


10y+(-2y)-3*20y^2=0

Wy multiply elements

-60y^2+10y+(-2y)=0

We get rid of parentheses

-60y^2+10y-2y=0

We add all the numbers together, and all the variables

-60y^2+8y=0

a = -60; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-60)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-60}=\frac{-16}{-120}
=2/15
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-60}=\frac{0}{-120}
=0
$