What is -5p^2+15000p>2000000 ?

The solution to -5p^2+15000p>2000000 is -100sqrt(185)+1500<p<100sqrt(185)+1500

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-5p^2+15000p>2000000

- 5 p^{2} + 15000 p > 2000000

- 100185 + 1500 < p < 100185 + 1500

Interval Notation

(- 100185 + 1500, 100185 + 1500)

Decimal Notation

139.85294 \dots < p < 2860.14705 \dots

Solution steps

- 5 p^{2} + 15000 p > 2000000

Rewrite in standard form

- p^{2} + 3000 p - 400000 > 0

Complete the square

- p^{2} + 3000 p - 400000 : - (p - 1500)^{2} + 1850000

- (p - 1500)^{2} + 1850000 > 0

Move

1850000

to the right side

- (p - 1500)^{2} > - 1850000

Multiply both sides by

- 1

(p - 1500)^{2} < 1850000

For

u^{n} < a

, if

n

is even then

- 1850000 < p - 1500 < 1850000

a < u < b

then

a < u and u < b

- 1850000 < p - 1500 and p - 1500 < 1850000

- 1850000 < p - 1500 : p > - 100185 + 1500

p - 1500 < 1850000 : p < 100185 + 1500

Combine the intervals

p > - 100185 + 1500 and p < 100185 + 1500

Merge Overlapping Intervals

- 100185 + 1500 < p < 100185 + 1500

(- 324)^{\frac{1}{4}}

2 + 4 x^{2} = 1

\frac{8}{5} - \frac{3}{2}

x^{2} = 8.33 \cdot 1 0^{- 4} (0.5 - x)

0 = x^{2} + 5 x - 6

What is -5p^2+15000p>2000000 ?
The solution to -5p^2+15000p>2000000 is -100sqrt(185)+1500<p<100sqrt(185)+1500