5-2/3x=1/2x+-4

Solution for 5-2/3x=1/2x+-4 equation:

5-2/3x=1/2x+-4

We move all terms to the left:

5-2/3x-(1/2x+-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+-4)!=0

x∈R


We add all the numbers together, and all the variables

-2/3x-(1/2x-4)+5=0

We get rid of parentheses

-2/3x-1/2x+4+5=0

We calculate fractions


(-4x)/6x^2+(-3x)/6x^2+4+5=0

We add all the numbers together, and all the variables

(-4x)/6x^2+(-3x)/6x^2+9=0

We multiply all the terms by the denominator


(-4x)+(-3x)+9*6x^2=0

Wy multiply elements

54x^2+(-4x)+(-3x)=0

We get rid of parentheses

54x^2-4x-3x=0

We add all the numbers together, and all the variables

54x^2-7x=0

a = 54; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·54·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*54}=\frac{0}{108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*54}=\frac{14}{108}
=7/54
$