2/6y=2y+6

Solution for 2/6y=2y+6 equation:

2/6y=2y+6

We move all terms to the left:

2/6y-(2y+6)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We get rid of parentheses

2/6y-2y-6=0

We multiply all the terms by the denominator


-2y*6y-6*6y+2=0

Wy multiply elements

-12y^2-36y+2=0

a = -12; b = -36; c = +2;
Δ = b2-4ac
Δ = -362-4·(-12)·2
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{87}}{2*-12}=\frac{36-4\sqrt{87}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{87}}{2*-12}=\frac{36+4\sqrt{87}}{-24}
$