X+1/24x=100

Solution for X+1/24x=100 equation:

X+1/24X=100

We move all terms to the left:

X+1/24X-(100)=0


Domain of the equation: 24X!=0

X!=0/24

X!=0

X∈R


We multiply all the terms by the denominator


X*24X-100*24X+1=0

Wy multiply elements

24X^2-2400X+1=0

a = 24; b = -2400; c = +1;
Δ = b2-4ac
Δ = -24002-4·24·1
Δ = 5759904
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:

$\sqrt{\Delta}=\sqrt{5759904}=\sqrt{16*359994}=\sqrt{16}*\sqrt{359994}=4\sqrt{359994}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2400)-4\sqrt{359994}}{2*24}=\frac{2400-4\sqrt{359994}}{48}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2400)+4\sqrt{359994}}{2*24}=\frac{2400+4\sqrt{359994}}{48}
$