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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


(-81x)/54x^2+2x/54x^2+4x/54x^2+4=0

We multiply all the terms by the denominator


(-81x)+2x+4x+4*54x^2=0

We add all the numbers together, and all the variables

6x+(-81x)+4*54x^2=0

Wy multiply elements

216x^2+6x+(-81x)=0

We get rid of parentheses

216x^2+6x-81x=0

We add all the numbers together, and all the variables

216x^2-75x=0

a = 216; b = -75; c = 0;
Δ = b2-4ac
Δ = -752-4·216·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-75}{2*216}=\frac{0}{432}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+75}{2*216}=\frac{150}{432}
=25/72
$