x+4/x=85

Solution for x+4/x=85 equation:

x+4/x=85

We move all terms to the left:

x+4/x-(85)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-85*x+4=0

We add all the numbers together, and all the variables

-85x+x*x+4=0

Wy multiply elements

x^2-85x+4=0

a = 1; b = -85; c = +4;
Δ = b2-4ac
Δ = -852-4·1·4
Δ = 7209
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:

$\sqrt{\Delta}=\sqrt{7209}=\sqrt{81*89}=\sqrt{81}*\sqrt{89}=9\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-9\sqrt{89}}{2*1}=\frac{85-9\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+9\sqrt{89}}{2*1}=\frac{85+9\sqrt{89}}{2}
$