1/2y-y=-1

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

1/2y-y=-1

We move all terms to the left:

1/2y-y-(-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

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -2; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-2)·1
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3}}{2*-2}=\frac{-2-2\sqrt{3}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3}}{2*-2}=\frac{-2+2\sqrt{3}}{-4}
$