What are the solutions to the equation 12x-x^2-19=0 ?

The solutions to the equation 12x-x^2-19=0 are x=6-sqrt(17),x=6+sqrt(17)

Find the zeros of 12x-x^2-19=0

The zeros of 12x-x^2-19=0 are x=6-sqrt(17),x=6+sqrt(17)

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12 x - x^{2} - 19 = 0

x = 6 - 17, x = 6 + 17

Decimal Notation

x = 1.87689 \dots, x = 10.12310 \dots

Solution steps

12 x - x^{2} - 19 = 0

Write in the standard form

a x^{2} + b x + c = 0

- x^{2} + 12 x - 19 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 ( - 1 ) ( - 19 )}{2 ( - 1 )}

1 2^{2} - 4 (- 1) (- 19) = 217

x_{1, 2} = \frac{- 12 \pm 2 17}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 12 + 2 17}{2 ( - 1 )}, x_{2} = \frac{- 12 - 2 17}{2 ( - 1 )}

x = \frac{- 12 + 2 17}{2 ( - 1 )} : 6 - 17

x = \frac{- 12 - 2 17}{2 ( - 1 )} : 6 + 17

The solutions to the quadratic equation are:

x = 6 - 17, x = 6 + 17

- x^{2} + 4 x = - 4 x + 3

- 9 x^{2} + 3 x + 10 = 0

9 p^{2} - 7 = 9 p

- 7 x^{2} + 12 x + 64 = 0

- 3 x^{2} - 9 = - 5 x

What are the solutions to the equation 12x-x^2-19=0 ?
The solutions to the equation 12x-x^2-19=0 are x=6-sqrt(17),x=6+sqrt(17)
Find the zeros of 12x-x^2-19=0
The zeros of 12x-x^2-19=0 are x=6-sqrt(17),x=6+sqrt(17)