1107,2=x^2+2x

Solution for 1107,2=x^2+2x equation:

1107.2=x^2+2x

We move all terms to the left:

1107.2-(x^2+2x)=0

We get rid of parentheses

-x^2-2x+1107.2=0

We add all the numbers together, and all the variables

-1x^2-2x+1107.2=0

a = -1; b = -2; c = +1107.2;
Δ = b2-4ac
Δ = -22-4·(-1)·1107.2
Δ = 4432.8
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{-(-2)-\sqrt{4432.8}}{2*-1}=\frac{2-\sqrt{4432.8}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{4432.8}}{2*-1}=\frac{2+\sqrt{4432.8}}{-2}
$