-1/3+2(1/2)p=3

Solution for -1/3+2(1/2)p=3 equation:

-1/3+2(1/2)p=3

We move all terms to the left:

-1/3+2(1/2)p-(3)=0


Domain of the equation: 2)p!=0

p!=0/1

p!=0

p∈R


determiningTheFunctionDomain
2(1/2)p-3-1/3=0

We add all the numbers together, and all the variables

2(+1/2)p-3-1/3=0

We multiply parentheses

2p^2-3-1/3=0

We multiply all the terms by the denominator


2p^2*3-1-3*3=0

We add all the numbers together, and all the variables

2p^2*3-10=0

Wy multiply elements

6p^2-10=0

a = 6; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·6·(-10)
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*6}=\frac{0-4\sqrt{15}}{12}
=-\frac{4\sqrt{15}}{12}
=-\frac{\sqrt{15}}{3}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*6}=\frac{0+4\sqrt{15}}{12}
=\frac{4\sqrt{15}}{12}
=\frac{\sqrt{15}}{3}
$