(X-1/x+2)=1.261859

Solution for (X-1/x+2)=1.261859 equation:

(X-1/X+2)=1.261859

We move all terms to the left:

(X-1/X+2)-(1.261859)=0


Domain of the equation: X+2)!=0

X∈R


We add all the numbers together, and all the variables

(X-1/X+2)-1.261859=0

We get rid of parentheses

X-1/X+2-1.261859=0

We multiply all the terms by the denominator


X*X+2*X-(1.261859)*X-1=0

We add all the numbers together, and all the variables

2X+X*X-(1.261859)*X-1=0

We multiply parentheses

2X+X*X-1.261859X-1=0

Wy multiply elements

X^2+2X-1.261859X-1=0

We add all the numbers together, and all the variables

X^2+0.738141X-1=0

a = 1; b = 0.738141; c = -1;
Δ = b2-4ac
Δ = 0.7381412-4·1·(-1)
Δ = 4.544852135881
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{-(0.738141)-\sqrt{4.544852135881}}{2*1}=\frac{-0.738141-\sqrt{4.544852135881}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.738141)+\sqrt{4.544852135881}}{2*1}=\frac{-0.738141+\sqrt{4.544852135881}}{2}
$