1/3y-4=1/10y

Solution for 1/3y-4=1/10y equation:

1/3y-4=1/10y

We move all terms to the left:

1/3y-4-(1/10y)=0


Domain of the equation: 3y!=0

y!=0/3

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

1/3y-(+1/10y)-4=0

We get rid of parentheses

1/3y-1/10y-4=0

We calculate fractions


10y/30y^2+(-3y)/30y^2-4=0

We multiply all the terms by the denominator


10y+(-3y)-4*30y^2=0

Wy multiply elements

-120y^2+10y+(-3y)=0

We get rid of parentheses

-120y^2+10y-3y=0

We add all the numbers together, and all the variables

-120y^2+7y=0

a = -120; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-120)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-120}=\frac{-14}{-240}
=7/120
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-120}=\frac{0}{-240}
=0
$