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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2-4x-1=0

a = 5; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·5·(-1)
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{-(-4)-6}{2*5}=\frac{-2}{10}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*5}=\frac{10}{10}
=1
$