2x-3=1/24x-12

Solution for 2x-3=1/24x-12 equation:

2x-3=1/24x-12

We move all terms to the left:

2x-3-(1/24x-12)=0


Domain of the equation: 24x-12)!=0

x∈R


We get rid of parentheses

2x-1/24x+12-3=0

We multiply all the terms by the denominator


2x*24x+12*24x-3*24x-1=0

Wy multiply elements

48x^2+288x-72x-1=0

We add all the numbers together, and all the variables

48x^2+216x-1=0

a = 48; b = 216; c = -1;
Δ = b2-4ac
Δ = 2162-4·48·(-1)
Δ = 46848
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:

$\sqrt{\Delta}=\sqrt{46848}=\sqrt{256*183}=\sqrt{256}*\sqrt{183}=16\sqrt{183}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-16\sqrt{183}}{2*48}=\frac{-216-16\sqrt{183}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+16\sqrt{183}}{2*48}=\frac{-216+16\sqrt{183}}{96}
$