x^2+x^-2-(11/4)=0

Solution for x^2+x^-2-(11/4)=0 equation:

x^2+x^-2-(11/4)=0

We add all the numbers together, and all the variables

x^2+x^-2-(+11/4)=0

We add all the numbers together, and all the variables

x^2+x-2-(+11/4)=0

We get rid of parentheses

x^2+x-2-11/4=0

We multiply all the terms by the denominator


x^2*4+x*4-11-2*4=0

We add all the numbers together, and all the variables

x^2*4+x*4-19=0

Wy multiply elements

4x^2+4x-19=0

a = 4; b = 4; c = -19;
Δ = b2-4ac
Δ = 42-4·4·(-19)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{5}}{2*4}=\frac{-4-8\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{5}}{2*4}=\frac{-4+8\sqrt{5}}{8}
$