P(x)=x(105-5x)-3(105-5x)

Solution for P(x)=x(105-5x)-3(105-5x) equation:

(P)=P(105-5P)-3(105-5P)

We move all terms to the left:

(P)-(P(105-5P)-3(105-5P))=0

We add all the numbers together, and all the variables

P-(P(-5P+105)-3(-5P+105))=0


We calculate terms in parentheses: -(P(-5P+105)-3(-5P+105)), so:

P(-5P+105)-3(-5P+105)

We multiply parentheses

-5P^2+105P+15P-315

We add all the numbers together, and all the variables

-5P^2+120P-315

Back to the equation:

-(-5P^2+120P-315)


We get rid of parentheses

5P^2-120P+P+315=0

We add all the numbers together, and all the variables

5P^2-119P+315=0

a = 5; b = -119; c = +315;
Δ = b2-4ac
Δ = -1192-4·5·315
Δ = 7861
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{-(-119)-\sqrt{7861}}{2*5}=\frac{119-\sqrt{7861}}{10}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+\sqrt{7861}}{2*5}=\frac{119+\sqrt{7861}}{10}
$