3y+9=1/4y

Solution for 3y+9=1/4y equation:

3y+9=1/4y

We move all terms to the left:

3y+9-(1/4y)=0


Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3y-(+1/4y)+9=0

We get rid of parentheses

3y-1/4y+9=0

We multiply all the terms by the denominator


3y*4y+9*4y-1=0

Wy multiply elements

12y^2+36y-1=0

a = 12; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·12·(-1)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-8\sqrt{21}}{2*12}=\frac{-36-8\sqrt{21}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+8\sqrt{21}}{2*12}=\frac{-36+8\sqrt{21}}{24}
$