1=1/2v-v

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

1=1/2v-v

We move all terms to the left:

1-(1/2v-v)=0


Domain of the equation: 2v-v)!=0

v∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1v-1/2v+1=0

We multiply all the terms by the denominator


1v*2v+1*2v-1=0

Wy multiply elements

2v^2+2v-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:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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