1/2y-2=2y-23

Solution for 1/2y-2=2y-23 equation:

1/2y-2=2y-23

We move all terms to the left:

1/2y-2-(2y-23)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-2y+23-2=0

We multiply all the terms by the denominator


-2y*2y+23*2y-2*2y+1=0

Wy multiply elements

-4y^2+46y-4y+1=0

We add all the numbers together, and all the variables

-4y^2+42y+1=0

a = -4; b = 42; c = +1;
Δ = b2-4ac
Δ = 422-4·(-4)·1
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{445}}{2*-4}=\frac{-42-2\sqrt{445}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{445}}{2*-4}=\frac{-42+2\sqrt{445}}{-8}
$