17y=85/y=5

Solution for 17y=85/y=5 equation:

17y=85/y=5

We move all terms to the left:

17y-(85/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

17y-(+85/y)=0

We get rid of parentheses

17y-85/y=0

We multiply all the terms by the denominator


17y*y-85=0

Wy multiply elements

17y^2-85=0

a = 17; b = 0; c = -85;
Δ = b2-4ac
Δ = 02-4·17·(-85)
Δ = 5780
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5780}=\sqrt{1156*5}=\sqrt{1156}*\sqrt{5}=34\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34\sqrt{5}}{2*17}=\frac{0-34\sqrt{5}}{34}
=-\frac{34\sqrt{5}}{34}
=-\sqrt{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34\sqrt{5}}{2*17}=\frac{0+34\sqrt{5}}{34}
=\frac{34\sqrt{5}}{34}
=\sqrt{5}
$