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^2-20y+1=0

a = -4; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-4)·1
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{26}}{2*-4}=\frac{20-4\sqrt{26}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{26}}{2*-4}=\frac{20+4\sqrt{26}}{-8}
$