3/16y=5/5y+65

Solution for 3/16y=5/5y+65 equation:

3/16y=5/5y+65

We move all terms to the left:

3/16y-(5/5y+65)=0


Domain of the equation: 16y!=0

y!=0/16

y!=0

y∈R



Domain of the equation: 5y+65)!=0

y∈R


We get rid of parentheses

3/16y-5/5y-65=0

We calculate fractions


15y/80y^2+(-80y)/80y^2-65=0

We multiply all the terms by the denominator


15y+(-80y)-65*80y^2=0

Wy multiply elements

-5200y^2+15y+(-80y)=0

We get rid of parentheses

-5200y^2+15y-80y=0

We add all the numbers together, and all the variables

-5200y^2-65y=0

a = -5200; b = -65; c = 0;
Δ = b2-4ac
Δ = -652-4·(-5200)·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*-5200}=\frac{0}{-10400}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+65}{2*-5200}=\frac{130}{-10400}
=-1/80
$