11-1/2y=3+6y

Solution for 11-1/2y=3+6y equation:

11-1/2y=3+6y

We move all terms to the left:

11-1/2y-(3+6y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-1/2y-(6y+3)+11=0

We get rid of parentheses

-1/2y-6y-3+11=0

We multiply all the terms by the denominator


-6y*2y-3*2y+11*2y-1=0

Wy multiply elements

-12y^2-6y+22y-1=0

We add all the numbers together, and all the variables

-12y^2+16y-1=0

a = -12; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·(-12)·(-1)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{13}}{2*-12}=\frac{-16-4\sqrt{13}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{13}}{2*-12}=\frac{-16+4\sqrt{13}}{-24}
$