9/x+x=83

Solution for 9/x+x=83 equation:

9/x+x=83

We move all terms to the left:

9/x+x-(83)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+9/x-83=0

We multiply all the terms by the denominator


x*x-83*x+9=0

We add all the numbers together, and all the variables

-83x+x*x+9=0

Wy multiply elements

x^2-83x+9=0

a = 1; b = -83; c = +9;
Δ = b2-4ac
Δ = -832-4·1·9
Δ = 6853
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-83)-\sqrt{6853}}{2*1}=\frac{83-\sqrt{6853}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+\sqrt{6853}}{2*1}=\frac{83+\sqrt{6853}}{2}
$