11.5=x+x^2

Solution for 11.5=x+x^2 equation:

11.5=x+x^2

We move all terms to the left:

11.5-(x+x^2)=0

We get rid of parentheses

-x^2-x+11.5=0

We add all the numbers together, and all the variables

-1x^2-1x+11.5=0

a = -1; b = -1; c = +11.5;
Δ = b2-4ac
Δ = -12-4·(-1)·11.5
Δ = 47
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{47}}{2*-1}=\frac{1-\sqrt{47}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{47}}{2*-1}=\frac{1+\sqrt{47}}{-2}
$