4(1/2x+4)=9(1/3x-2)

Solution for 4(1/2x+4)=9(1/3x-2) equation:

4(1/2x+4)=9(1/3x-2)

We move all terms to the left:

4(1/2x+4)-(9(1/3x-2))=0


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

x∈R



Domain of the equation: 3x-2))!=0

x∈R


We multiply parentheses

4x-(9(1/3x-2))+16=0

We multiply all the terms by the denominator


4x*3x+16*3x-2))-(9(1-2))=0

We add all the numbers together, and all the variables

4x*3x+16*3x-2))-(9(-1))=0

We add all the numbers together, and all the variables

4x*3x+16*3x=0

Wy multiply elements

12x^2+48x=0

a = 12; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·12·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*12}=\frac{-96}{24}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*12}=\frac{0}{24}
=0
$