4/3x-4=40-2x

Solution for 4/3x-4=40-2x equation:

4/3x-4=40-2x

We move all terms to the left:

4/3x-4-(40-2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(-2x+40)-4=0

We get rid of parentheses

4/3x+2x-40-4=0

We multiply all the terms by the denominator


2x*3x-40*3x-4*3x+4=0

Wy multiply elements

6x^2-120x-12x+4=0

We add all the numbers together, and all the variables

6x^2-132x+4=0

a = 6; b = -132; c = +4;
Δ = b2-4ac
Δ = -1322-4·6·4
Δ = 17328
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:

$\sqrt{\Delta}=\sqrt{17328}=\sqrt{5776*3}=\sqrt{5776}*\sqrt{3}=76\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-76\sqrt{3}}{2*6}=\frac{132-76\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+76\sqrt{3}}{2*6}=\frac{132+76\sqrt{3}}{12}
$