1/2x+4=-31/3x

Solution for 1/2x+4=-31/3x equation:

1/2x+4=-31/3x

We move all terms to the left:

1/2x+4-(-31/3x)=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 get rid of parentheses

1/2x+31/3x+4=0

We calculate fractions


3x/6x^2+62x/6x^2+4=0

We multiply all the terms by the denominator


3x+62x+4*6x^2=0

We add all the numbers together, and all the variables

65x+4*6x^2=0

Wy multiply elements

24x^2+65x=0

a = 24; b = 65; c = 0;
Δ = b2-4ac
Δ = 652-4·24·0
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-65}{2*24}=\frac{-130}{48}
=-2+17/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+65}{2*24}=\frac{0}{48}
=0
$