1/3y+31/5y=5

Solution for 1/3y+31/5y=5 equation:

1/3y+31/5y=5

We move all terms to the left:

1/3y+31/5y-(5)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We calculate fractions


5y/15y^2+93y/15y^2-5=0

We multiply all the terms by the denominator


5y+93y-5*15y^2=0

We add all the numbers together, and all the variables

98y-5*15y^2=0

Wy multiply elements

-75y^2+98y=0

a = -75; b = 98; c = 0;
Δ = b2-4ac
Δ = 982-4·(-75)·0
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-98}{2*-75}=\frac{-196}{-150}
=1+23/75
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+98}{2*-75}=\frac{0}{-150}
=0
$