X+1/9x=70

Solution for X+1/9x=70 equation:

X+1/9X=70

We move all terms to the left:

X+1/9X-(70)=0


Domain of the equation: 9X!=0

X!=0/9

X!=0

X∈R


We multiply all the terms by the denominator


X*9X-70*9X+1=0

Wy multiply elements

9X^2-630X+1=0

a = 9; b = -630; c = +1;
Δ = b2-4ac
Δ = -6302-4·9·1
Δ = 396864
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:

$\sqrt{\Delta}=\sqrt{396864}=\sqrt{576*689}=\sqrt{576}*\sqrt{689}=24\sqrt{689}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-24\sqrt{689}}{2*9}=\frac{630-24\sqrt{689}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+24\sqrt{689}}{2*9}=\frac{630+24\sqrt{689}}{18}
$