2000/b+b=90

Solution for 2000/b+b=90 equation:

2000/b+b=90

We move all terms to the left:

2000/b+b-(90)=0


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

b+2000/b-90=0

We multiply all the terms by the denominator


b*b-90*b+2000=0

We add all the numbers together, and all the variables

-90b+b*b+2000=0

Wy multiply elements

b^2-90b+2000=0

a = 1; b = -90; c = +2000;
Δ = b2-4ac
Δ = -902-4·1·2000
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10}{2*1}=\frac{80}{2}
=40
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10}{2*1}=\frac{100}{2}
=50
$