1/2y+11=2y

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

1/2y+11=2y

We move all terms to the left:

1/2y+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

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -4; b = 22; c = +1;
Δ = b2-4ac
Δ = 222-4·(-4)·1
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-10\sqrt{5}}{2*-4}=\frac{-22-10\sqrt{5}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+10\sqrt{5}}{2*-4}=\frac{-22+10\sqrt{5}}{-8}
$