P(x)=-5x^2+230x-2240

Solution for P(x)=-5x^2+230x-2240 equation:

(P)=-5P^2+230P-2240

We move all terms to the left:

(P)-(-5P^2+230P-2240)=0

We get rid of parentheses

5P^2-230P+P+2240=0

We add all the numbers together, and all the variables

5P^2-229P+2240=0

a = 5; b = -229; c = +2240;
Δ = b2-4ac
Δ = -2292-4·5·2240
Δ = 7641
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:

$\sqrt{\Delta}=\sqrt{7641}=\sqrt{9*849}=\sqrt{9}*\sqrt{849}=3\sqrt{849}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-229)-3\sqrt{849}}{2*5}=\frac{229-3\sqrt{849}}{10}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-229)+3\sqrt{849}}{2*5}=\frac{229+3\sqrt{849}}{10}
$