2/3x-41/2x=-8

Solution for 2/3x-41/2x=-8 equation:

2/3x-41/2x=-8

We move all terms to the left:

2/3x-41/2x-(-8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-41/2x+8=0

We calculate fractions


4x/6x^2+(-123x)/6x^2+8=0

We multiply all the terms by the denominator


4x+(-123x)+8*6x^2=0

Wy multiply elements

48x^2+4x+(-123x)=0

We get rid of parentheses

48x^2+4x-123x=0

We add all the numbers together, and all the variables

48x^2-119x=0

a = 48; b = -119; c = 0;
Δ = b2-4ac
Δ = -1192-4·48·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-119}{2*48}=\frac{0}{96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+119}{2*48}=\frac{238}{96}
=2+23/48
$