1/2x+3-2/3x=1/2

Solution for 1/2x+3-2/3x=1/2 equation:

1/2x+3-2/3x=1/2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


3x/24x^2+(-16x)/24x^2+(-3x)/24x^2+3=0

We multiply all the terms by the denominator


3x+(-16x)+(-3x)+3*24x^2=0

Wy multiply elements

72x^2+3x+(-16x)+(-3x)=0

We get rid of parentheses

72x^2+3x-16x-3x=0

We add all the numbers together, and all the variables

72x^2-16x=0

a = 72; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·72·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*72}=\frac{32}{144}
=2/9
$