P(x)=4x/x+5

Solution for P(x)=4x/x+5 equation:

(P)=4P/P+5

We move all terms to the left:

(P)-(4P/P+5)=0


Domain of the equation: P+5)!=0

P∈R


We get rid of parentheses

P-4P/P-5=0

We multiply all the terms by the denominator


P*P-4P-5*P=0

We add all the numbers together, and all the variables

-9P+P*P=0

Wy multiply elements

P^2-9P=0

a = 1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·1·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*1}=\frac{0}{2}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*1}=\frac{18}{2}
=9
$