x2+6x+1=-2x+1

Solution for x2+6x+1=-2x+1 equation:

x2+6x+1=-2x+1

We move all terms to the left:

x2+6x+1-(-2x+1)=0

We add all the numbers together, and all the variables

x^2+6x-(-2x+1)+1=0

We get rid of parentheses

x^2+6x+2x-1+1=0

We add all the numbers together, and all the variables

x^2+8x=0

a = 1; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·1·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*1}=\frac{0}{2}
=0
$