(1/2)x-(1/3)=2

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

(1/2)x-(1/3)=2

We move all terms to the left:

(1/2)x-(1/3)-(2)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


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

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2-2-(+1/3)=0

We get rid of parentheses

x^2-2-1/3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x^2*3-7=0

Wy multiply elements

3x^2-7=0

a = 3; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·3·(-7)
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*3}=\frac{0-2\sqrt{21}}{6}
=-\frac{2\sqrt{21}}{6}
=-\frac{\sqrt{21}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*3}=\frac{0+2\sqrt{21}}{6}
=\frac{2\sqrt{21}}{6}
=\frac{\sqrt{21}}{3}
$