P(x)=x(72-4x)-(121+12x)

Solution for P(x)=x(72-4x)-(121+12x) equation:

(P)=P(72-4P)-(121+12P)

We move all terms to the left:

(P)-(P(72-4P)-(121+12P))=0

We add all the numbers together, and all the variables

P-(P(-4P+72)-(12P+121))=0


We calculate terms in parentheses: -(P(-4P+72)-(12P+121)), so:

P(-4P+72)-(12P+121)

We multiply parentheses

-4P^2+72P-(12P+121)

We get rid of parentheses

-4P^2+72P-12P-121

We add all the numbers together, and all the variables

-4P^2+60P-121

Back to the equation:

-(-4P^2+60P-121)


We get rid of parentheses

4P^2-60P+P+121=0

We add all the numbers together, and all the variables

4P^2-59P+121=0

a = 4; b = -59; c = +121;
Δ = b2-4ac
Δ = -592-4·4·121
Δ = 1545
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{-(-59)-\sqrt{1545}}{2*4}=\frac{59-\sqrt{1545}}{8}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{1545}}{2*4}=\frac{59+\sqrt{1545}}{8}
$