8/y+4y=12

Solution for 8/y+4y=12 equation:

8/y+4y=12

We move all terms to the left:

8/y+4y-(12)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

4y+8/y-12=0

We multiply all the terms by the denominator


4y*y-12*y+8=0

We add all the numbers together, and all the variables

-12y+4y*y+8=0

Wy multiply elements

4y^2-12y+8=0

a = 4; b = -12; c = +8;
Δ = b2-4ac
Δ = -122-4·4·8
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4}{2*4}=\frac{8}{8}
=1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4}{2*4}=\frac{16}{8}
=2
$