(1)/(2)x-4=-3-(1)/(3)x

Solution for (1)/(2)x-4=-3-(1)/(3)x equation:

(1)/(2)x-4=-3-(1)/(3)x

We move all terms to the left:

(1)/(2)x-4-(-3-(1)/(3)x)=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^2-1=0

We multiply all the terms by the denominator


3x+2x-1*6x^2=0

We add all the numbers together, and all the variables

5x-1*6x^2=0

Wy multiply elements

-6x^2+5x=0

a = -6; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-6)·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*-6}=\frac{-10}{-12}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-6}=\frac{0}{-12}
=0
$