x+20/x+50=0.83

Solution for x+20/x+50=0.83 equation:

x+20/x+50=0.83

We move all terms to the left:

x+20/x+50-(0.83)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+20/x+49.17=0

We multiply all the terms by the denominator


x*x+(49.17)*x+20=0

We multiply parentheses

x*x+49.17x+20=0

Wy multiply elements

x^2+49.17x+20=0

a = 1; b = 49.17; c = +20;
Δ = b2-4ac
Δ = 49.172-4·1·20
Δ = 2337.6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49.17)-\sqrt{2337.6889}}{2*1}=\frac{-49.17-\sqrt{2337.6889}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49.17)+\sqrt{2337.6889}}{2*1}=\frac{-49.17+\sqrt{2337.6889}}{2}
$