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

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

1/2X+1-1/3X+1=3

We move all terms to the left:

1/2X+1-1/3X+1-(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 add all the numbers together, and all the variables

1/2X-1/3X-1=0

We calculate fractions


3X/6X^2+(-2X)/6X^2-1=0

We multiply all the terms by the denominator


3X+(-2X)-1*6X^2=0

Wy multiply elements

-6X^2+3X+(-2X)=0

We get rid of parentheses

-6X^2+3X-2X=0

We add all the numbers together, and all the variables

-6X^2+X=0

a = -6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-6)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-6}=\frac{-2}{-12}
=1/6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-6}=\frac{0}{-12}
=0
$