1/2X+4=-3-1/3x

Solution for 1/2X+4=-3-1/3x equation:

1/2X+4=-3-1/3X

We move all terms to the left:

1/2X+4-(-3-1/3X)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R



Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

1/2X-(-1/3X-3)+4=0

We get rid of parentheses

1/2X+1/3X+3+4=0

We calculate fractions


3X/6X^2+2X/6X^2+3+4=0

We add all the numbers together, and all the variables

3X/6X^2+2X/6X^2+7=0

We multiply all the terms by the denominator


3X+2X+7*6X^2=0

We add all the numbers together, and all the variables

5X+7*6X^2=0

Wy multiply elements

42X^2+5X=0

a = 42; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·42·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*42}=\frac{-10}{84}
=-5/42
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*42}=\frac{0}{84}
=0
$