0=3x+24/3x-24

Solution for 0=3x+24/3x-24 equation:

0=3x+24/3x-24

We move all terms to the left:

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


Domain of the equation: 3x-24)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2+72x-24=0

a = -9; b = 72; c = -24;
Δ = b2-4ac
Δ = 722-4·(-9)·(-24)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{30}}{2*-9}=\frac{-72-12\sqrt{30}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{30}}{2*-9}=\frac{-72+12\sqrt{30}}{-18}
$