1/2+1/5y=2/15y+1

Solution for 1/2+1/5y=2/15y+1 equation:

1/2+1/5y=2/15y+1

We move all terms to the left:

1/2+1/5y-(2/15y+1)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 15y+1)!=0

y∈R


We get rid of parentheses

1/5y-2/15y-1+1/2=0

We calculate fractions


75y^2/300y^2+60y/300y^2+(-40y)/300y^2-1=0

We multiply all the terms by the denominator


75y^2+60y+(-40y)-1*300y^2=0

Wy multiply elements

75y^2-300y^2+60y+(-40y)=0

We get rid of parentheses

75y^2-300y^2+60y-40y=0

We add all the numbers together, and all the variables

-225y^2+20y=0

a = -225; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-225)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-225}=\frac{-40}{-450}
=4/45
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-225}=\frac{0}{-450}
=0
$