X+1/8x=18

Solution for X+1/8x=18 equation:

X+1/8X=18

We move all terms to the left:

X+1/8X-(18)=0


Domain of the equation: 8X!=0

X!=0/8

X!=0

X∈R


We multiply all the terms by the denominator


X*8X-18*8X+1=0

Wy multiply elements

8X^2-144X+1=0

a = 8; b = -144; c = +1;
Δ = b2-4ac
Δ = -1442-4·8·1
Δ = 20704
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:

$\sqrt{\Delta}=\sqrt{20704}=\sqrt{16*1294}=\sqrt{16}*\sqrt{1294}=4\sqrt{1294}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1294}}{2*8}=\frac{144-4\sqrt{1294}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1294}}{2*8}=\frac{144+4\sqrt{1294}}{16}
$