10+1/3y=1+2/5y

Solution for 10+1/3y=1+2/5y equation:

10+1/3y=1+2/5y

We move all terms to the left:

10+1/3y-(1+2/5y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/3y-(2/5y+1)+10=0

We get rid of parentheses

1/3y-2/5y-1+10=0

We calculate fractions


5y/15y^2+(-6y)/15y^2-1+10=0

We add all the numbers together, and all the variables

5y/15y^2+(-6y)/15y^2+9=0

We multiply all the terms by the denominator


5y+(-6y)+9*15y^2=0

Wy multiply elements

135y^2+5y+(-6y)=0

We get rid of parentheses

135y^2+5y-6y=0

We add all the numbers together, and all the variables

135y^2-1y=0

a = 135; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·135·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*135}=\frac{0}{270}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*135}=\frac{2}{270}
=1/135
$