8-3y/5y+2y=1/17

Solution for 8-3y/5y+2y=1/17 equation:

8-3y/5y+2y=1/17

We move all terms to the left:

8-3y/5y+2y-(1/17)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-3y/5y+2y+8-(+1/17)=0

We add all the numbers together, and all the variables

2y-3y/5y+8-(+1/17)=0

We get rid of parentheses

2y-3y/5y+8-1/17=0

We calculate fractions


2y+(-51y)/85y+(-5y)/85y+8=0

We multiply all the terms by the denominator


2y*85y+(-51y)+(-5y)+8*85y=0

Wy multiply elements

170y^2+(-51y)+(-5y)+680y=0

We get rid of parentheses

170y^2-51y-5y+680y=0

We add all the numbers together, and all the variables

170y^2+624y=0

a = 170; b = 624; c = 0;
Δ = b2-4ac
Δ = 6242-4·170·0
Δ = 389376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{389376}=624$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(624)-624}{2*170}=\frac{-1248}{340}
=-3+57/85
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(624)+624}{2*170}=\frac{0}{340}
=0
$