x-1/3x=24

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

x-1/3x=24

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


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}
$