2/3x=24+6x

Solution for 2/3x=24+6x equation:

2/3x=24+6x

We move all terms to the left:

2/3x-(24+6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(6x+24)=0

We get rid of parentheses

2/3x-6x-24=0

We multiply all the terms by the denominator


-6x*3x-24*3x+2=0

Wy multiply elements

-18x^2-72x+2=0

a = -18; b = -72; c = +2;
Δ = b2-4ac
Δ = -722-4·(-18)·2
Δ = 5328
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:

$\sqrt{\Delta}=\sqrt{5328}=\sqrt{144*37}=\sqrt{144}*\sqrt{37}=12\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{37}}{2*-18}=\frac{72-12\sqrt{37}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{37}}{2*-18}=\frac{72+12\sqrt{37}}{-36}
$