What are the solutions to the equation 200=-1/6 x^2+100x ?

The solutions to the equation 200=-1/6 x^2+100x are x=20(15-sqrt(222)),x=20(15+sqrt(222))

Find the zeros of 200=-1/6 x^2+100x

The zeros of 200=-1/6 x^2+100x are x=20(15-sqrt(222)),x=20(15+sqrt(222))

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200 = - \frac{1}{6} x^{2} + 100 x

x = 20 (15 - 222), x = 20 (15 + 222)

Decimal Notation

x = 2.00671 \dots, x = 597.99328 \dots

Solution steps

200 = - \frac{1}{6} x^{2} + 100 x

Multiply both sides by

6

1200 = - x^{2} + 600 x

Switch sides

- x^{2} + 600 x = 1200

Move

1200

to the left side

- x^{2} + 600 x - 1200 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 600 \pm 60 0 ^{2} - 4 ( - 1 ) ( - 1200 )}{2 ( - 1 )}

60 0^{2} - 4 (- 1) (- 1200) = 40222

x_{1, 2} = \frac{- 600 \pm 40 222}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 600 + 40 222}{2 ( - 1 )}, x_{2} = \frac{- 600 - 40 222}{2 ( - 1 )}

x = \frac{- 600 + 40 222}{2 ( - 1 )} : 20 (15 - 222)

x = \frac{- 600 - 40 222}{2 ( - 1 )} : 20 (15 + 222)

The solutions to the quadratic equation are:

x = 20 (15 - 222), x = 20 (15 + 222)

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What are the solutions to the equation 200=-1/6 x^2+100x ?
The solutions to the equation 200=-1/6 x^2+100x are x=20(15-sqrt(222)),x=20(15+sqrt(222))
Find the zeros of 200=-1/6 x^2+100x
The zeros of 200=-1/6 x^2+100x are x=20(15-sqrt(222)),x=20(15+sqrt(222))