4-2/3x=1/2x+16

Solution for 4-2/3x=1/2x+16 equation:

4-2/3x=1/2x+16

We move all terms to the left:

4-2/3x-(1/2x+16)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+16)!=0

x∈R


We get rid of parentheses

-2/3x-1/2x-16+4=0

We calculate fractions


(-4x)/6x^2+(-3x)/6x^2-16+4=0

We add all the numbers together, and all the variables

(-4x)/6x^2+(-3x)/6x^2-12=0

We multiply all the terms by the denominator


(-4x)+(-3x)-12*6x^2=0

Wy multiply elements

-72x^2+(-4x)+(-3x)=0

We get rid of parentheses

-72x^2-4x-3x=0

We add all the numbers together, and all the variables

-72x^2-7x=0

a = -72; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-72)·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*-72}=\frac{0}{-144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-72}=\frac{14}{-144}
=-7/72
$