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

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

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

We move all terms to the left:

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


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


3x*4x-8*4x-8-3))-(4(-3))=0

We add all the numbers together, and all the variables

3x*4x-8*4x=0

Wy multiply elements

12x^2-32x=0

a = 12; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·12·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*12}=\frac{64}{24}
=2+2/3
$