1/3x-24=2x-1

Solution for 1/3x-24=2x-1 equation:

1/3x-24=2x-1

We move all terms to the left:

1/3x-24-(2x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2x+1-24=0

We multiply all the terms by the denominator


-2x*3x+1*3x-24*3x+1=0

Wy multiply elements

-6x^2+3x-72x+1=0

We add all the numbers together, and all the variables

-6x^2-69x+1=0

a = -6; b = -69; c = +1;
Δ = b2-4ac
Δ = -692-4·(-6)·1
Δ = 4785
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-\sqrt{4785}}{2*-6}=\frac{69-\sqrt{4785}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{4785}}{2*-6}=\frac{69+\sqrt{4785}}{-12}
$