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

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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} $

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