1/12x-x-24=0

Solution for 1/12x-x-24=0 equation:

1/12x-x-24=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2-288x+1=0

a = -12; b = -288; c = +1;
Δ = b2-4ac
Δ = -2882-4·(-12)·1
Δ = 82992
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:

$\sqrt{\Delta}=\sqrt{82992}=\sqrt{16*5187}=\sqrt{16}*\sqrt{5187}=4\sqrt{5187}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-4\sqrt{5187}}{2*-12}=\frac{288-4\sqrt{5187}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+4\sqrt{5187}}{2*-12}=\frac{288+4\sqrt{5187}}{-24}
$