3/5-15/y=3/4y

Solution for 3/5-15/y=3/4y equation:

3/5-15/y=3/4y

We move all terms to the left:

3/5-15/y-(3/4y)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-15/y-(+3/4y)+3/5=0

We get rid of parentheses

-15/y-3/4y+3/5=0

We calculate fractions


48y^2/100y^2+(-1500y)/100y^2+(-75y)/100y^2=0

We multiply all the terms by the denominator


48y^2+(-1500y)+(-75y)=0

We get rid of parentheses

48y^2-1500y-75y=0

We add all the numbers together, and all the variables

48y^2-1575y=0

a = 48; b = -1575; c = 0;
Δ = b2-4ac
Δ = -15752-4·48·0
Δ = 2480625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2480625}=1575$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1575)-1575}{2*48}=\frac{0}{96}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1575)+1575}{2*48}=\frac{3150}{96}
=32+13/16
$