X+1/9x=90

Solution for X+1/9x=90 equation:

X+1/9X=90

We move all terms to the left:

X+1/9X-(90)=0


Domain of the equation: 9X!=0

X!=0/9

X!=0

X∈R


We multiply all the terms by the denominator


X*9X-90*9X+1=0

Wy multiply elements

9X^2-810X+1=0

a = 9; b = -810; c = +1;
Δ = b2-4ac
Δ = -8102-4·9·1
Δ = 656064
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:

$\sqrt{\Delta}=\sqrt{656064}=\sqrt{576*1139}=\sqrt{576}*\sqrt{1139}=24\sqrt{1139}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-810)-24\sqrt{1139}}{2*9}=\frac{810-24\sqrt{1139}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-810)+24\sqrt{1139}}{2*9}=\frac{810+24\sqrt{1139}}{18}
$