16/y*2-3y=13

Solution for 16/y*2-3y=13 equation:

16/y*2-3y=13

We move all terms to the left:

16/y*2-3y-(13)=0


Domain of the equation: y*2!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-3y+16/y*2-13=0

We multiply all the terms by the denominator


-3y*y*2-13*y*2+16=0

Wy multiply elements

-6y^2*2-26y*2+16=0

Wy multiply elements

-12y^2-52y+16=0

a = -12; b = -52; c = +16;
Δ = b2-4ac
Δ = -522-4·(-12)·16
Δ = 3472
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:

$\sqrt{\Delta}=\sqrt{3472}=\sqrt{16*217}=\sqrt{16}*\sqrt{217}=4\sqrt{217}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{217}}{2*-12}=\frac{52-4\sqrt{217}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{217}}{2*-12}=\frac{52+4\sqrt{217}}{-24}
$