x^2+2x+1=18.75

Solution for x^2+2x+1=18.75 equation:

x^2+2x+1=18.75

We move all terms to the left:

x^2+2x+1-(18.75)=0

We add all the numbers together, and all the variables

x^2+2x-17.75=0

a = 1; b = 2; c = -17.75;
Δ = b2-4ac
Δ = 22-4·1·(-17.75)
Δ = 75
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:

$\sqrt{\Delta}=\sqrt{75}=\sqrt{25*3}=\sqrt{25}*\sqrt{3}=5\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-5\sqrt{3}}{2*1}=\frac{-2-5\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+5\sqrt{3}}{2*1}=\frac{-2+5\sqrt{3}}{2}
$