P(x)=-0.25X^2+23.50X-210

Solution for P(x)=-0.25X^2+23.50X-210 equation:

(P)=-0.25P^2+23.50P-210

We move all terms to the left:

(P)-(-0.25P^2+23.50P-210)=0

We get rid of parentheses

0.25P^2-23.50P+P+210=0

We add all the numbers together, and all the variables

0.25P^2-22.5P+210=0

a = 0.25; b = -22.5; c = +210;
Δ = b2-4ac
Δ = -22.52-4·0.25·210
Δ = 296.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22.5)-\sqrt{296.25}}{2*0.25}=\frac{22.5-\sqrt{296.25}}{0.5}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22.5)+\sqrt{296.25}}{2*0.25}=\frac{22.5+\sqrt{296.25}}{0.5}
$