14/6y+1=2y-4

Solution for 14/6y+1=2y-4 equation:

14/6y+1=2y-4

We move all terms to the left:

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


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


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+30y+14=0

a = -12; b = 30; c = +14;
Δ = b2-4ac
Δ = 302-4·(-12)·14
Δ = 1572
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:

$\sqrt{\Delta}=\sqrt{1572}=\sqrt{4*393}=\sqrt{4}*\sqrt{393}=2\sqrt{393}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{393}}{2*-12}=\frac{-30-2\sqrt{393}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{393}}{2*-12}=\frac{-30+2\sqrt{393}}{-24}
$