P(x)=-x^2+14x+58

Solution for P(x)=-x^2+14x+58 equation:

(P)=-P^2+14P+58

We move all terms to the left:

(P)-(-P^2+14P+58)=0

We get rid of parentheses

P^2-14P+P-58=0

We add all the numbers together, and all the variables

P^2-13P-58=0

a = 1; b = -13; c = -58;
Δ = b2-4ac
Δ = -132-4·1·(-58)
Δ = 401
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{-(-13)-\sqrt{401}}{2*1}=\frac{13-\sqrt{401}}{2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{401}}{2*1}=\frac{13+\sqrt{401}}{2}
$