(x+1)2=5x2+x+1

Solution for (x+1)2=5x2+x+1 equation:

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2+x+1=0

a = -5; b = 1; c = +1;
Δ = b2-4ac
Δ = 12-4·(-5)·1
Δ = 21
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{-(1)-\sqrt{21}}{2*-5}=\frac{-1-\sqrt{21}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{21}}{2*-5}=\frac{-1+\sqrt{21}}{-10}
$