P=230+20x-0.5x^2

Solution for P=230+20x-0.5x^2 equation:

=230+20P-0.5P^2

We move all terms to the left:

-(230+20P-0.5P^2)=0

We get rid of parentheses

0.5P^2-20P-230=0

a = 0.5; b = -20; c = -230;
Δ = b2-4ac
Δ = -202-4·0.5·(-230)
Δ = 860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{860}=\sqrt{4*215}=\sqrt{4}*\sqrt{215}=2\sqrt{215}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{215}}{2*0.5}=\frac{20-2\sqrt{215}}{1}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{215}}{2*0.5}=\frac{20+2\sqrt{215}}{1}
$