4(1/2x-3)=8(2-3/4x)

Solution for 4(1/2x-3)=8(2-3/4x) equation:

4(1/2x-3)=8(2-3/4x)

We move all terms to the left:

4(1/2x-3)-(8(2-3/4x))=0


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

x∈R



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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4(1/2x-3)-(8(-3/4x+2))=0

We multiply parentheses

4x-(8(-3/4x+2))-12=0

We multiply all the terms by the denominator


4x*4x-12*4x-3+2))-(8(+2))=0

We add all the numbers together, and all the variables

4x*4x-12*4x-3+2))-(82)=0

We add all the numbers together, and all the variables

4x*4x-12*4x=0

Wy multiply elements

16x^2-48x=0

a = 16; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·16·0
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*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*16}=\frac{96}{32}
=3
$