x=15-0.5*(x^2)

Solution for x=15-0.5*(x^2) equation:

x=15-0.5(x^2)

We move all terms to the left:

x-(15-0.5(x^2))=0

determiningTheFunctionDomain
-(15-0.5x^2)+x=0

We get rid of parentheses

0.5x^2+x-15=0

a = 0.5; b = 1; c = -15;
Δ = b2-4ac
Δ = 12-4·0.5·(-15)
Δ = 31
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{31}}{2*0.5}=\frac{-1-\sqrt{31}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{31}}{2*0.5}=\frac{-1+\sqrt{31}}{1}
$