X+1/10x=82

Solution for X+1/10x=82 equation:

X+1/10X=82

We move all terms to the left:

X+1/10X-(82)=0


Domain of the equation: 10X!=0

X!=0/10

X!=0

X∈R


We multiply all the terms by the denominator


X*10X-82*10X+1=0

Wy multiply elements

10X^2-820X+1=0

a = 10; b = -820; c = +1;
Δ = b2-4ac
Δ = -8202-4·10·1
Δ = 672360
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:

$\sqrt{\Delta}=\sqrt{672360}=\sqrt{4*168090}=\sqrt{4}*\sqrt{168090}=2\sqrt{168090}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-820)-2\sqrt{168090}}{2*10}=\frac{820-2\sqrt{168090}}{20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-820)+2\sqrt{168090}}{2*10}=\frac{820+2\sqrt{168090}}{20}
$