3x^-2=2-0.25x^2

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

3x^-2=2-0.25x^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

0.25x^2+3x-4=0

a = 0.25; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·0.25·(-4)
Δ = 13
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{13}}{2*0.25}=\frac{-3-\sqrt{13}}{0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{13}}{2*0.25}=\frac{-3+\sqrt{13}}{0.5}
$