1/x+x-90=0

Solution for 1/x+x-90=0 equation:

1/x+x-90=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x-90=0

We multiply all the terms by the denominator


x*x-90*x+1=0

We add all the numbers together, and all the variables

-90x+x*x+1=0

Wy multiply elements

x^2-90x+1=0

a = 1; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·1·1
Δ = 8096
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:

$\sqrt{\Delta}=\sqrt{8096}=\sqrt{16*506}=\sqrt{16}*\sqrt{506}=4\sqrt{506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-4\sqrt{506}}{2*1}=\frac{90-4\sqrt{506}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+4\sqrt{506}}{2*1}=\frac{90+4\sqrt{506}}{2}
$