11.5=16x+x^2

Solution for 11.5=16x+x^2 equation:

11.5=16x+x^2

We move all terms to the left:

11.5-(16x+x^2)=0

We get rid of parentheses

-x^2-16x+11.5=0

We add all the numbers together, and all the variables

-1x^2-16x+11.5=0

a = -1; b = -16; c = +11.5;
Δ = b2-4ac
Δ = -162-4·(-1)·11.5
Δ = 302
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{-(-16)-\sqrt{302}}{2*-1}=\frac{16-\sqrt{302}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+\sqrt{302}}{2*-1}=\frac{16+\sqrt{302}}{-2}
$