(2/3x)+24=2x

Solution for (2/3x)+24=2x equation:

(2/3x)+24=2x

We move all terms to the left:

(2/3x)+24-(2x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/3x)-2x+24=0

We add all the numbers together, and all the variables

-2x+(+2/3x)+24=0

We get rid of parentheses

-2x+2/3x+24=0

We multiply all the terms by the denominator


-2x*3x+24*3x+2=0

Wy multiply elements

-6x^2+72x+2=0

a = -6; b = 72; c = +2;
Δ = b2-4ac
Δ = 722-4·(-6)·2
Δ = 5232
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:

$\sqrt{\Delta}=\sqrt{5232}=\sqrt{16*327}=\sqrt{16}*\sqrt{327}=4\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{327}}{2*-6}=\frac{-72-4\sqrt{327}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{327}}{2*-6}=\frac{-72+4\sqrt{327}}{-12}
$