1/3x-8=3x+24

Solution for 1/3x-8=3x+24 equation:

1/3x-8=3x+24

We move all terms to the left:

1/3x-8-(3x+24)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-3x-24-8=0

We multiply all the terms by the denominator


-3x*3x-24*3x-8*3x+1=0

Wy multiply elements

-9x^2-72x-24x+1=0

We add all the numbers together, and all the variables

-9x^2-96x+1=0

a = -9; b = -96; c = +1;
Δ = b2-4ac
Δ = -962-4·(-9)·1
Δ = 9252
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:

$\sqrt{\Delta}=\sqrt{9252}=\sqrt{36*257}=\sqrt{36}*\sqrt{257}=6\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-6\sqrt{257}}{2*-9}=\frac{96-6\sqrt{257}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+6\sqrt{257}}{2*-9}=\frac{96+6\sqrt{257}}{-18}
$