5x^2+2x+1=x^2+1

Solution for 5x^2+2x+1=x^2+1 equation:

5x^2+2x+1=x^2+1

We move all terms to the left:

5x^2+2x+1-(x^2+1)=0

We get rid of parentheses

5x^2-x^2+2x-1+1=0

We add all the numbers together, and all the variables

4x^2+2x=0

a = 4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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