1/2y+11=2y-1

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

1/2y+11=2y-1

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-4y^2+24y+1=0

a = -4; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-4)·1
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{37}}{2*-4}=\frac{-24-4\sqrt{37}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{37}}{2*-4}=\frac{-24+4\sqrt{37}}{-8}
$