x+4/x=90

Solution for x+4/x=90 equation:

x+4/x=90

We move all terms to the left:

x+4/x-(90)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-90*x+4=0

We add all the numbers together, and all the variables

-90x+x*x+4=0

Wy multiply elements

x^2-90x+4=0

a = 1; b = -90; c = +4;
Δ = b2-4ac
Δ = -902-4·1·4
Δ = 8084
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:

$\sqrt{\Delta}=\sqrt{8084}=\sqrt{4*2021}=\sqrt{4}*\sqrt{2021}=2\sqrt{2021}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2021}}{2*1}=\frac{90-2\sqrt{2021}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2021}}{2*1}=\frac{90+2\sqrt{2021}}{2}
$