1/23x-24=3x

Solution for 1/23x-24=3x equation:

1/23x-24=3x

We move all terms to the left:

1/23x-24-(3x)=0


Domain of the equation: 23x!=0

x!=0/23

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+1/23x-24=0

We multiply all the terms by the denominator


-3x*23x-24*23x+1=0

Wy multiply elements

-69x^2-552x+1=0

a = -69; b = -552; c = +1;
Δ = b2-4ac
Δ = -5522-4·(-69)·1
Δ = 304980
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:

$\sqrt{\Delta}=\sqrt{304980}=\sqrt{4*76245}=\sqrt{4}*\sqrt{76245}=2\sqrt{76245}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-552)-2\sqrt{76245}}{2*-69}=\frac{552-2\sqrt{76245}}{-138}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-552)+2\sqrt{76245}}{2*-69}=\frac{552+2\sqrt{76245}}{-138}
$