11/4y-11/20y-7/15=14/3

Solution for 11/4y-11/20y-7/15=14/3 equation:

11/4y-11/20y-7/15=14/3

We move all terms to the left:

11/4y-11/20y-7/15-(14/3)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 20y!=0

y!=0/20

y!=0

y∈R


We add all the numbers together, and all the variables

11/4y-11/20y-7/15-(+14/3)=0

We get rid of parentheses

11/4y-11/20y-7/15-14/3=0

We calculate fractions


(-3360y^2)/3600y^2+(-33600y^2)/3600y^2+9900y/3600y^2+(-1980y)/3600y^2=0

We multiply all the terms by the denominator


(-3360y^2)+(-33600y^2)+9900y+(-1980y)=0

We get rid of parentheses

-3360y^2-33600y^2+9900y-1980y=0

We add all the numbers together, and all the variables

-36960y^2+7920y=0

a = -36960; b = 7920; c = 0;
Δ = b2-4ac
Δ = 79202-4·(-36960)·0
Δ = 62726400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{62726400}=7920$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7920)-7920}{2*-36960}=\frac{-15840}{-73920}
=3/14
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7920)+7920}{2*-36960}=\frac{0}{-73920}
=0
$