1/24x-6=3x+8

Solution for 1/24x-6=3x+8 equation:

1/24x-6=3x+8

We move all terms to the left:

1/24x-6-(3x+8)=0


Domain of the equation: 24x!=0

x!=0/24

x!=0

x∈R


We get rid of parentheses

1/24x-3x-8-6=0

We multiply all the terms by the denominator


-3x*24x-8*24x-6*24x+1=0

Wy multiply elements

-72x^2-192x-144x+1=0

We add all the numbers together, and all the variables

-72x^2-336x+1=0

a = -72; b = -336; c = +1;
Δ = b2-4ac
Δ = -3362-4·(-72)·1
Δ = 113184
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:

$\sqrt{\Delta}=\sqrt{113184}=\sqrt{144*786}=\sqrt{144}*\sqrt{786}=12\sqrt{786}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-12\sqrt{786}}{2*-72}=\frac{336-12\sqrt{786}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+12\sqrt{786}}{2*-72}=\frac{336+12\sqrt{786}}{-144}
$