P=25x(10x+250)

Solution for P=25x(10x+250) equation:

=25P(10P+250)

We move all terms to the left:

-(25P(10P+250))=0


We calculate terms in parentheses: -(25P(10P+250)), so:

25P(10P+250)

We multiply parentheses

250P^2+6250P

Back to the equation:

-(250P^2+6250P)


We get rid of parentheses

-250P^2-6250P=0

a = -250; b = -6250; c = 0;
Δ = b2-4ac
Δ = -62502-4·(-250)·0
Δ = 39062500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39062500}=6250$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6250)-6250}{2*-250}=\frac{0}{-500}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6250)+6250}{2*-250}=\frac{12500}{-500}
=-25
$