3(x^-2)=2-0.25x^2

Solution for 3(x^-2)=2-0.25x^2 equation:

3(x^-2)=2-0.25x^2

We move all terms to the left:

3(x^-2)-(2-0.25x^2)=0

We multiply parentheses

-(2-0.25x^2)+3x-6=0

We get rid of parentheses

0.25x^2+3x-2-6=0

We add all the numbers together, and all the variables

0.25x^2+3x-8=0

a = 0.25; b = 3; c = -8;
Δ = b2-4ac
Δ = 32-4·0.25·(-8)
Δ = 17
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{-(3)-\sqrt{17}}{2*0.25}=\frac{-3-\sqrt{17}}{0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{17}}{2*0.25}=\frac{-3+\sqrt{17}}{0.5}
$