P(x)=7+5x-4x^2

Solution for P(x)=7+5x-4x^2 equation:

(P)=7+5P-4P^2

We move all terms to the left:

(P)-(7+5P-4P^2)=0

We get rid of parentheses

4P^2-5P+P-7=0

We add all the numbers together, and all the variables

4P^2-4P-7=0

a = 4; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·4·(-7)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{2}}{2*4}=\frac{4-8\sqrt{2}}{8}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{2}}{2*4}=\frac{4+8\sqrt{2}}{8}
$