P=x(-45x+1250)-10(-45x+1250)

Solution for P=x(-45x+1250)-10(-45x+1250) equation:

=P(-45P+1250)-10(-45P+1250)

We move all terms to the left:

-(P(-45P+1250)-10(-45P+1250))=0


We calculate terms in parentheses: -(P(-45P+1250)-10(-45P+1250)), so:

P(-45P+1250)-10(-45P+1250)

We multiply parentheses

-45P^2+1250P+450P-12500

We add all the numbers together, and all the variables

-45P^2+1700P-12500

Back to the equation:

-(-45P^2+1700P-12500)


We get rid of parentheses

45P^2-1700P+12500=0

a = 45; b = -1700; c = +12500;
Δ = b2-4ac
Δ = -17002-4·45·12500
Δ = 640000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{640000}=800$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1700)-800}{2*45}=\frac{900}{90}
=10
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1700)+800}{2*45}=\frac{2500}{90}
=27+7/9
$