44/6y+4/2=2y-3

Solution for 44/6y+4/2=2y-3 equation:

44/6y+4/2=2y-3

We move all terms to the left:

44/6y+4/2-(2y-3)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

44/6y-(2y-3)+2=0

We get rid of parentheses

44/6y-2y+3+2=0

We multiply all the terms by the denominator


-2y*6y+3*6y+2*6y+44=0

Wy multiply elements

-12y^2+18y+12y+44=0

We add all the numbers together, and all the variables

-12y^2+30y+44=0

a = -12; b = 30; c = +44;
Δ = b2-4ac
Δ = 302-4·(-12)·44
Δ = 3012
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:

$\sqrt{\Delta}=\sqrt{3012}=\sqrt{4*753}=\sqrt{4}*\sqrt{753}=2\sqrt{753}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{753}}{2*-12}=\frac{-30-2\sqrt{753}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{753}}{2*-12}=\frac{-30+2\sqrt{753}}{-24}
$