30000=1000(30+17t-t^2)

Solution for 30000=1000(30+17t-t^2) equation:

30000=1000(30+17t-t^2)

We move all terms to the left:

30000-(1000(30+17t-t^2))=0


We calculate terms in parentheses: -(1000(30+17t-t^2)), so:

1000(30+17t-t^2)

We multiply parentheses

-1000t^2+17000t+30000

Back to the equation:

-(-1000t^2+17000t+30000)


We get rid of parentheses

1000t^2-17000t-30000+30000=0

We add all the numbers together, and all the variables

1000t^2-17000t=0

a = 1000; b = -17000; c = 0;
Δ = b2-4ac
Δ = -170002-4·1000·0
Δ = 289000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289000000}=17000$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17000)-17000}{2*1000}=\frac{0}{2000}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17000)+17000}{2*1000}=\frac{34000}{2000}
=17
$