1/3x+24=3x

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

1/3x+24=3x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -9; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-9)·1
Δ = 5220
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:

$\sqrt{\Delta}=\sqrt{5220}=\sqrt{36*145}=\sqrt{36}*\sqrt{145}=6\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-6\sqrt{145}}{2*-9}=\frac{-72-6\sqrt{145}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+6\sqrt{145}}{2*-9}=\frac{-72+6\sqrt{145}}{-18}
$