2(x^2+1/x^2)-7(x+1/x)+9=0

Solution for 2(x^2+1/x^2)-7(x+1/x)+9=0 equation:

2(x^2+1/x^2)-7(x+1/x)+9=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

2(x^2+1/x^2)-7(+x+1/x)+9=0

We multiply parentheses

2x^2+2x-7x-7x+9=0

We add all the numbers together, and all the variables

2x^2-12x+9=0

a = 2; b = -12; c = +9;
Δ = b2-4ac
Δ = -122-4·2·9
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{2}}{2*2}=\frac{12-6\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{2}}{2*2}=\frac{12+6\sqrt{2}}{4}
$