11/15y+13/5y+7/15=7/3

Solution for 11/15y+13/5y+7/15=7/3 equation:

11/15y+13/5y+7/15=7/3

We move all terms to the left:

11/15y+13/5y+7/15-(7/3)=0


Domain of the equation: 15y!=0

y!=0/15

y!=0

y∈R



Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

11/15y+13/5y+7/15-(+7/3)=0

We get rid of parentheses

11/15y+13/5y+7/15-7/3=0

We calculate fractions


(-39375y^2)/3375y^2+495y/3375y^2+8775y/3375y^2+315y/3375y^2=0

We multiply all the terms by the denominator


(-39375y^2)+495y+8775y+315y=0

We add all the numbers together, and all the variables

(-39375y^2)+9585y=0

We get rid of parentheses

-39375y^2+9585y=0

a = -39375; b = 9585; c = 0;
Δ = b2-4ac
Δ = 95852-4·(-39375)·0
Δ = 91872225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{91872225}=9585$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9585)-9585}{2*-39375}=\frac{-19170}{-78750}
=213/875
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9585)+9585}{2*-39375}=\frac{0}{-78750}
=0
$