8/x+x=90

Solution for 8/x+x=90 equation:

8/x+x=90

We move all terms to the left:

8/x+x-(90)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+8/x-90=0

We multiply all the terms by the denominator


x*x-90*x+8=0

We add all the numbers together, and all the variables

-90x+x*x+8=0

Wy multiply elements

x^2-90x+8=0

a = 1; b = -90; c = +8;
Δ = b2-4ac
Δ = -902-4·1·8
Δ = 8068
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:

$\sqrt{\Delta}=\sqrt{8068}=\sqrt{4*2017}=\sqrt{4}*\sqrt{2017}=2\sqrt{2017}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2017}}{2*1}=\frac{90-2\sqrt{2017}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2017}}{2*1}=\frac{90+2\sqrt{2017}}{2}
$