What are the solutions to the equation 30x-0.24x^2=275+12x ?

The solutions to the equation 30x-0.24x^2=275+12x are x=(25(9-sqrt(15)))/6 ,x=(25(9+sqrt(15)))/6

Find the zeros of 30x-0.24x^2=275+12x

The zeros of 30x-0.24x^2=275+12x are x=(25(9-sqrt(15)))/6 ,x=(25(9+sqrt(15)))/6

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30 x - 0.24 x^{2} = 275 + 12 x

x = \frac{25 ( 9 - 15 )}{6}, x = \frac{25 ( 9 + 15 )}{6}

Decimal Notation

x = 21.36256 \dots, x = 53.63743 \dots

Solution steps

30 x - 0.24 x^{2} = 275 + 12 x

Multiply both sides by

100

3000 x - 24 x^{2} = 27500 + 1200 x

Move

1200 x

to the left side

- 24 x^{2} + 1800 x = 27500

Move

27500

to the left side

- 24 x^{2} + 1800 x - 27500 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 1800 \pm 180 0 ^{2} - 4 ( - 24 ) ( - 27500 )}{2 ( - 24 )}

180 0^{2} - 4 (- 24) (- 27500) = 20015

x_{1, 2} = \frac{- 1800 \pm 200 15}{2 ( - 24 )}

Separate the solutions

x_{1} = \frac{- 1800 + 200 15}{2 ( - 24 )}, x_{2} = \frac{- 1800 - 200 15}{2 ( - 24 )}

x = \frac{- 1800 + 200 15}{2 ( - 24 )} : \frac{25 ( 9 - 15 )}{6}

x = \frac{- 1800 - 200 15}{2 ( - 24 )} : \frac{25 ( 9 + 15 )}{6}

The solutions to the quadratic equation are:

x = \frac{25 ( 9 - 15 )}{6}, x = \frac{25 ( 9 + 15 )}{6}

x (x + 5) = - 6

x + 4 = x^{2} - 2 x

- 6 x^{2} - 96 x - 330 = 0

- 3 x^{2} - 6 x + 3 = 0

1 1^{2} + c^{2} = 1 5^{2}

What are the solutions to the equation 30x-0.24x^2=275+12x ?
The solutions to the equation 30x-0.24x^2=275+12x are x=(25(9-sqrt(15)))/6 ,x=(25(9+sqrt(15)))/6
Find the zeros of 30x-0.24x^2=275+12x
The zeros of 30x-0.24x^2=275+12x are x=(25(9-sqrt(15)))/6 ,x=(25(9+sqrt(15)))/6