P=50,000(2t-1)(t-5)

Solution for P=50,000(2t-1)(t-5) equation:

=50.000(2P-1)(P-5)

We move all terms to the left:

-(50.000(2P-1)(P-5))=0

We multiply parentheses ..

-(50.000(+2P^2-10P-1P+5))=0


We calculate terms in parentheses: -(50.000(+2P^2-10P-1P+5)), so:

50.000(+2P^2-10P-1P+5)

We multiply parentheses

100P^2-500P-50P+250

We add all the numbers together, and all the variables

100P^2-550P+250

Back to the equation:

-(100P^2-550P+250)


We get rid of parentheses

-100P^2+550P-250=0

a = -100; b = 550; c = -250;
Δ = b2-4ac
Δ = 5502-4·(-100)·(-250)
Δ = 202500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{202500}=450$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(550)-450}{2*-100}=\frac{-1000}{-200}
=+5
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(550)+450}{2*-100}=\frac{-100}{-200}
=1/2
$