P(x)=510-30x-480/x

Solution for P(x)=510-30x-480/x equation:

(P)=510-30P-480/P

We move all terms to the left:

(P)-(510-30P-480/P)=0


Domain of the equation: P)!=0

P!=0/1

P!=0

P∈R


We add all the numbers together, and all the variables

P-(-30P-480/P+510)=0

We get rid of parentheses

P+30P+480/P-510=0

We multiply all the terms by the denominator


P*P+30P*P-510*P+480=0

We add all the numbers together, and all the variables

-510P+P*P+30P*P+480=0

Wy multiply elements

P^2+30P^2-510P+480=0

We add all the numbers together, and all the variables

31P^2-510P+480=0

a = 31; b = -510; c = +480;
Δ = b2-4ac
Δ = -5102-4·31·480
Δ = 200580
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:

$\sqrt{\Delta}=\sqrt{200580}=\sqrt{4*50145}=\sqrt{4}*\sqrt{50145}=2\sqrt{50145}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-510)-2\sqrt{50145}}{2*31}=\frac{510-2\sqrt{50145}}{62}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-510)+2\sqrt{50145}}{2*31}=\frac{510+2\sqrt{50145}}{62}
$