5(x^2+1/x^2)-12(x+1/x)-11=0

Solution for 5(x^2+1/x^2)-12(x+1/x)-11=0 equation:

5(x^2+1/x^2)-12(x+1/x)-11=0


Domain of the equation: x^2)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5(x^2+1/x^2)-12(+x+1/x)-11=0

We multiply parentheses

5x^2+5x-12x-12x-11=0

We add all the numbers together, and all the variables

5x^2-19x-11=0

a = 5; b = -19; c = -11;
Δ = b2-4ac
Δ = -192-4·5·(-11)
Δ = 581
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{-(-19)-\sqrt{581}}{2*5}=\frac{19-\sqrt{581}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{581}}{2*5}=\frac{19+\sqrt{581}}{10}
$