3y+3/y+3=27

Solution for 3y+3/y+3=27 equation:

3y+3/y+3=27

We move all terms to the left:

3y+3/y+3-(27)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

3y+3/y-24=0

We multiply all the terms by the denominator


3y*y-24*y+3=0

We add all the numbers together, and all the variables

-24y+3y*y+3=0

Wy multiply elements

3y^2-24y+3=0

a = 3; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·3·3
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{15}}{2*3}=\frac{24-6\sqrt{15}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{15}}{2*3}=\frac{24+6\sqrt{15}}{6}
$