14/6y+2/2=2y+4

Solution for 14/6y+2/2=2y+4 equation:

14/6y+2/2=2y+4

We move all terms to the left:

14/6y+2/2-(2y+4)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

14/6y-(2y+4)+1=0

We get rid of parentheses

14/6y-2y-4+1=0

We multiply all the terms by the denominator


-2y*6y-4*6y+1*6y+14=0

Wy multiply elements

-12y^2-24y+6y+14=0

We add all the numbers together, and all the variables

-12y^2-18y+14=0

a = -12; b = -18; c = +14;
Δ = b2-4ac
Δ = -182-4·(-12)·14
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{249}}{2*-12}=\frac{18-2\sqrt{249}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{249}}{2*-12}=\frac{18+2\sqrt{249}}{-24}
$