92/y+2y=40

Solution for 92/y+2y=40 equation:

92/y+2y=40

We move all terms to the left:

92/y+2y-(40)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

2y+92/y-40=0

We multiply all the terms by the denominator


2y*y-40*y+92=0

We add all the numbers together, and all the variables

-40y+2y*y+92=0

Wy multiply elements

2y^2-40y+92=0

a = 2; b = -40; c = +92;
Δ = b2-4ac
Δ = -402-4·2·92
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-12\sqrt{6}}{2*2}=\frac{40-12\sqrt{6}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+12\sqrt{6}}{2*2}=\frac{40+12\sqrt{6}}{4}
$