(4/3x-8)-2x=44

Solution for (4/3x-8)-2x=44 equation:

(4/3x-8)-2x=44

We move all terms to the left:

(4/3x-8)-2x-(44)=0


Domain of the equation: 3x-8)!=0

x∈R


We add all the numbers together, and all the variables

-2x+(4/3x-8)-44=0

We get rid of parentheses

-2x+4/3x-8-44=0

We multiply all the terms by the denominator


-2x*3x-8*3x-44*3x+4=0

Wy multiply elements

-6x^2-24x-132x+4=0

We add all the numbers together, and all the variables

-6x^2-156x+4=0

a = -6; b = -156; c = +4;
Δ = b2-4ac
Δ = -1562-4·(-6)·4
Δ = 24432
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:

$\sqrt{\Delta}=\sqrt{24432}=\sqrt{16*1527}=\sqrt{16}*\sqrt{1527}=4\sqrt{1527}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-4\sqrt{1527}}{2*-6}=\frac{156-4\sqrt{1527}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+4\sqrt{1527}}{2*-6}=\frac{156+4\sqrt{1527}}{-12}
$