12y/y+4y^2/y=0

Solution for 12y/y+4y^2/y=0 equation:

12y/y+4y^2/y=0


Domain of the equation: y!=0

y∈R


We multiply all the terms by the denominator


4y^2+12y=0

a = 4; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·4·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*4}=\frac{-24}{8}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*4}=\frac{0}{8}
=0
$