4-4X^2=1-x^2

Solution for 4-4X^2=1-x^2 equation:

4-4X^2=1-X^2

We move all terms to the left:

4-4X^2-(1-X^2)=0

We get rid of parentheses

-4X^2+X^2-1+4=0

We add all the numbers together, and all the variables

-3X^2+3=0

a = -3; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-3)·3
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-3}=\frac{-6}{-6}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-3}=\frac{6}{-6}
=-1
$