1/2y+6=11-2y

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

1/2y+6=11-2y

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4y^2-22y+12y+1=0

We add all the numbers together, and all the variables

4y^2-10y+1=0

a = 4; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·4·1
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*4}=\frac{10-2\sqrt{21}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*4}=\frac{10+2\sqrt{21}}{8}
$