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

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

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

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

-4x-(+2/3x)+32+8=0

We get rid of parentheses

-4x-2/3x+32+8=0

We multiply all the terms by the denominator


-4x*3x+32*3x+8*3x-2=0

Wy multiply elements

-12x^2+96x+24x-2=0

We add all the numbers together, and all the variables

-12x^2+120x-2=0

a = -12; b = 120; c = -2;
Δ = b2-4ac
Δ = 1202-4·(-12)·(-2)
Δ = 14304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14304}=\sqrt{16*894}=\sqrt{16}*\sqrt{894}=4\sqrt{894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{894}}{2*-12}=\frac{-120-4\sqrt{894}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{894}}{2*-12}=\frac{-120+4\sqrt{894}}{-24}
$