2/3y+1/5y=15

Solution for 2/3y+1/5y=15 equation:

2/3y+1/5y=15

We move all terms to the left:

2/3y+1/5y-(15)=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


10y/15y^2+3y/15y^2-15=0

We multiply all the terms by the denominator


10y+3y-15*15y^2=0

We add all the numbers together, and all the variables

13y-15*15y^2=0

Wy multiply elements

-225y^2+13y=0

a = -225; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-225)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-225}=\frac{-26}{-450}
=13/225
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-225}=\frac{0}{-450}
=0
$