36+4y=84/y=

Solution for 36+4y=84/y= equation:

36+4y=84/y=

We move all terms to the left:

36+4y-(84/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

4y-(+84/y)+36=0

We get rid of parentheses

4y-84/y+36=0

We multiply all the terms by the denominator


4y*y+36*y-84=0

We add all the numbers together, and all the variables

36y+4y*y-84=0

Wy multiply elements

4y^2+36y-84=0

a = 4; b = 36; c = -84;
Δ = b2-4ac
Δ = 362-4·4·(-84)
Δ = 2640
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:

$\sqrt{\Delta}=\sqrt{2640}=\sqrt{16*165}=\sqrt{16}*\sqrt{165}=4\sqrt{165}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{165}}{2*4}=\frac{-36-4\sqrt{165}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{165}}{2*4}=\frac{-36+4\sqrt{165}}{8}
$