20+x=2/x+1

Solution for 20+x=2/x+1 equation:

20+x=2/x+1

We move all terms to the left:

20+x-(2/x+1)=0


Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

x-2/x-1+20=0

We multiply all the terms by the denominator


x*x-1*x+20*x-2=0

We add all the numbers together, and all the variables

19x+x*x-2=0

Wy multiply elements

x^2+19x-2=0

a = 1; b = 19; c = -2;
Δ = b2-4ac
Δ = 192-4·1·(-2)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-3\sqrt{41}}{2*1}=\frac{-19-3\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+3\sqrt{41}}{2*1}=\frac{-19+3\sqrt{41}}{2}
$