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

Solution for 2/3-3/2x-1/3x-4=0 equation:

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 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

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

Wy multiply elements

-216x^2+4x+(-81x)+(-2x)=0

We get rid of parentheses

-216x^2+4x-81x-2x=0

We add all the numbers together, and all the variables

-216x^2-79x=0

a = -216; b = -79; c = 0;
Δ = b2-4ac
Δ = -792-4·(-216)·0
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-79}{2*-216}=\frac{0}{-432}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+79}{2*-216}=\frac{158}{-432}
=-79/216
$