2/5y+7/15y-9=30

Solution for 2/5y+7/15y-9=30 equation:

2/5y+7/15y-9=30

We move all terms to the left:

2/5y+7/15y-9-(30)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 15y!=0

y!=0/15

y!=0

y∈R


We add all the numbers together, and all the variables

2/5y+7/15y-39=0

We calculate fractions


30y/75y^2+35y/75y^2-39=0

We multiply all the terms by the denominator


30y+35y-39*75y^2=0

We add all the numbers together, and all the variables

65y-39*75y^2=0

Wy multiply elements

-2925y^2+65y=0

a = -2925; b = 65; c = 0;
Δ = b2-4ac
Δ = 652-4·(-2925)·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-65}{2*-2925}=\frac{-130}{-5850}
=1/45
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+65}{2*-2925}=\frac{0}{-5850}
=0
$