2=1/4x^2+1

Solution for 2=1/4x^2+1 equation:

2=1/4x^2+1

We move all terms to the left:

2-(1/4x^2+1)=0


Domain of the equation: 4x^2+1)!=0

x∈R


We get rid of parentheses

-1/4x^2-1+2=0

We multiply all the terms by the denominator


-1*4x^2+2*4x^2-1=0

Wy multiply elements

-4x^2+8x^2-1=0

We add all the numbers together, and all the variables

4x^2-1=0

a = 4; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·4·(-1)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*4}=\frac{4}{8}
=1/2
$