2(x2+1/x2)-9(x+1/x)+14=0

Solution for 2(x2+1/x2)-9(x+1/x)+14=0 equation:

2(x2+1/x2)-9(x+1/x)+14=0


Domain of the equation: x2)!=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

2(+x^2+1/x2)-9(+x+1/x)+14=0

We multiply parentheses

2x^2+2x-9x-9x+14=0

We add all the numbers together, and all the variables

2x^2-16x+14=0

a = 2; b = -16; c = +14;
Δ = b2-4ac
Δ = -162-4·2·14
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12}{2*2}=\frac{28}{4}
=7
$