-1/2y+2y=1

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

-1/2y+2y=1

We move all terms to the left:

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

We multiply all the terms by the denominator


2y*2y-1*2y-1=0

Wy multiply elements

4y^2-2y-1=0

a = 4; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·4·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5}}{2*4}=\frac{2-2\sqrt{5}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5}}{2*4}=\frac{2+2\sqrt{5}}{8}
$