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

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

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

We move all terms to the left:

1/2x+1/3x-(1/2-3)=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 get rid of parentheses

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

We calculate fractions


3x/24x^2+8x/24x^2+(-3x)/24x^2+3=0

We multiply all the terms by the denominator


3x+8x+(-3x)+3*24x^2=0

We add all the numbers together, and all the variables

11x+(-3x)+3*24x^2=0

Wy multiply elements

72x^2+11x+(-3x)=0

We get rid of parentheses

72x^2+11x-3x=0

We add all the numbers together, and all the variables

72x^2+8x=0

a = 72; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·72·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*72}=\frac{-16}{144}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*72}=\frac{0}{144}
=0
$