3=3y-34/y+16

Solution for 3=3y-34/y+16 equation:

3=3y-34/y+16

We move all terms to the left:

3-(3y-34/y+16)=0


Domain of the equation: y+16)!=0

y∈R


We get rid of parentheses

-3y+34/y-16+3=0

We multiply all the terms by the denominator


-3y*y-16*y+3*y+34=0

We add all the numbers together, and all the variables

-13y-3y*y+34=0

Wy multiply elements

-3y^2-13y+34=0

a = -3; b = -13; c = +34;
Δ = b2-4ac
Δ = -132-4·(-3)·34
Δ = 577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{577}}{2*-3}=\frac{13-\sqrt{577}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{577}}{2*-3}=\frac{13+\sqrt{577}}{-6}
$