(5+x)=x^2+3x+1

Solution for (5+x)=x^2+3x+1 equation:

(5+x)=x^2+3x+1

We move all terms to the left:

(5+x)-(x^2+3x+1)=0

We add all the numbers together, and all the variables

(x+5)-(x^2+3x+1)=0

We get rid of parentheses

-x^2+x-3x+5-1=0

We add all the numbers together, and all the variables

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

a = -1; b = -2; c = +4;
Δ = b2-4ac
Δ = -22-4·(-1)·4
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5}}{2*-1}=\frac{2-2\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5}}{2*-1}=\frac{2+2\sqrt{5}}{-2}
$