P(300)=-0.5(x)^2+400(x)-6,000

Solution for P(300)=-0.5(x)^2+400(x)-6,000 equation:

(300)=-0.5(P)^2+400(P)-6.000

We move all terms to the left:

(300)-(-0.5(P)^2+400(P)-6.000)=0

We get rid of parentheses

0.5P^2-400P+6.000+300=0

We add all the numbers together, and all the variables

0.5P^2-400P+306=0

a = 0.5; b = -400; c = +306;
Δ = b2-4ac
Δ = -4002-4·0.5·306
Δ = 159388
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:

$\sqrt{\Delta}=\sqrt{159388}=\sqrt{4*39847}=\sqrt{4}*\sqrt{39847}=2\sqrt{39847}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-2\sqrt{39847}}{2*0.5}=\frac{400-2\sqrt{39847}}{1}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+2\sqrt{39847}}{2*0.5}=\frac{400+2\sqrt{39847}}{1}
$