1/3x=x-24

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

1/3x=x-24

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-x+24=0

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+72x+1=0

a = -3; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-3)·1
Δ = 5196
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:

$\sqrt{\Delta}=\sqrt{5196}=\sqrt{4*1299}=\sqrt{4}*\sqrt{1299}=2\sqrt{1299}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1299}}{2*-3}=\frac{-72-2\sqrt{1299}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1299}}{2*-3}=\frac{-72+2\sqrt{1299}}{-6}
$