P(x)=4x^2-35x-375

Solution for P(x)=4x^2-35x-375 equation:

(P)=4P^2-35P-375

We move all terms to the left:

(P)-(4P^2-35P-375)=0

We get rid of parentheses

-4P^2+P+35P+375=0

We add all the numbers together, and all the variables

-4P^2+36P+375=0

a = -4; b = 36; c = +375;
Δ = b2-4ac
Δ = 362-4·(-4)·375
Δ = 7296
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:

$\sqrt{\Delta}=\sqrt{7296}=\sqrt{64*114}=\sqrt{64}*\sqrt{114}=8\sqrt{114}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-8\sqrt{114}}{2*-4}=\frac{-36-8\sqrt{114}}{-8}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+8\sqrt{114}}{2*-4}=\frac{-36+8\sqrt{114}}{-8}
$