12x-24=1/2x+8

Solution for 12x-24=1/2x+8 equation:

12x-24=1/2x+8

We move all terms to the left:

12x-24-(1/2x+8)=0


Domain of the equation: 2x+8)!=0

x∈R


We get rid of parentheses

12x-1/2x-8-24=0

We multiply all the terms by the denominator


12x*2x-8*2x-24*2x-1=0

Wy multiply elements

24x^2-16x-48x-1=0

We add all the numbers together, and all the variables

24x^2-64x-1=0

a = 24; b = -64; c = -1;
Δ = b2-4ac
Δ = -642-4·24·(-1)
Δ = 4192
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:

$\sqrt{\Delta}=\sqrt{4192}=\sqrt{16*262}=\sqrt{16}*\sqrt{262}=4\sqrt{262}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{262}}{2*24}=\frac{64-4\sqrt{262}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{262}}{2*24}=\frac{64+4\sqrt{262}}{48}
$