11/6y-2=1/4y+6

Solution for 11/6y-2=1/4y+6 equation:

11/6y-2=1/4y+6

We move all terms to the left:

11/6y-2-(1/4y+6)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 4y+6)!=0

y∈R


We get rid of parentheses

11/6y-1/4y-6-2=0

We calculate fractions


44y/24y^2+(-6y)/24y^2-6-2=0

We add all the numbers together, and all the variables

44y/24y^2+(-6y)/24y^2-8=0

We multiply all the terms by the denominator


44y+(-6y)-8*24y^2=0

Wy multiply elements

-192y^2+44y+(-6y)=0

We get rid of parentheses

-192y^2+44y-6y=0

We add all the numbers together, and all the variables

-192y^2+38y=0

a = -192; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-192)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-192}=\frac{-76}{-384}
=19/96
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-192}=\frac{0}{-384}
=0
$