X+1/8x=126

Solution for X+1/8x=126 equation:

X+1/8X=126

We move all terms to the left:

X+1/8X-(126)=0


Domain of the equation: 8X!=0

X!=0/8

X!=0

X∈R


We multiply all the terms by the denominator


X*8X-126*8X+1=0

Wy multiply elements

8X^2-1008X+1=0

a = 8; b = -1008; c = +1;
Δ = b2-4ac
Δ = -10082-4·8·1
Δ = 1016032
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:

$\sqrt{\Delta}=\sqrt{1016032}=\sqrt{16*63502}=\sqrt{16}*\sqrt{63502}=4\sqrt{63502}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1008)-4\sqrt{63502}}{2*8}=\frac{1008-4\sqrt{63502}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1008)+4\sqrt{63502}}{2*8}=\frac{1008+4\sqrt{63502}}{16}
$