2/3y+3/5y=114

Solution for 2/3y+3/5y=114 equation:

2/3y+3/5y=114

We move all terms to the left:

2/3y+3/5y-(114)=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+9y/15y^2-114=0

We multiply all the terms by the denominator


10y+9y-114*15y^2=0

We add all the numbers together, and all the variables

19y-114*15y^2=0

Wy multiply elements

-1710y^2+19y=0

a = -1710; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-1710)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-1710}=\frac{-38}{-3420}
=1/90
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-1710}=\frac{0}{-3420}
=0
$