What are the solutions to the equation -3x^2+9x=1 ?

The solutions to the equation -3x^2+9x=1 are x=(9-sqrt(69))/6 ,x=(9+sqrt(69))/6

Find the zeros of -3x^2+9x=1

The zeros of -3x^2+9x=1 are x=(9-sqrt(69))/6 ,x=(9+sqrt(69))/6

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- 3 x^{2} + 9 x = 1

x = \frac{9 - 69}{6}, x = \frac{9 + 69}{6}

Decimal

x = 0.11556 \dots, x = 2.88443 \dots

Solution steps

- 3 x^{2} + 9 x = 1

Move

1

to the left side

- 3 x^{2} + 9 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 ( - 3 ) ( - 1 )}{2 ( - 3 )}

9^{2} - 4 (- 3) (- 1) = 69

x_{1, 2} = \frac{- 9 \pm 69}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- 9 + 69}{2 ( - 3 )}, x_{2} = \frac{- 9 - 69}{2 ( - 3 )}

x = \frac{- 9 + 69}{2 ( - 3 )} : \frac{9 - 69}{6}

x = \frac{- 9 - 69}{2 ( - 3 )} : \frac{9 + 69}{6}

The solutions to the quadratic equation are:

x = \frac{9 - 69}{6}, x = \frac{9 + 69}{6}

- 3 x^{2} + 9 x = 7

x^{2} + 1 = 4 x + 3

5 x^{2} - 5 x - 30 = 0

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

12 x^{2} + 6 x = 5

What are the solutions to the equation -3x^2+9x=1 ?
The solutions to the equation -3x^2+9x=1 are x=(9-sqrt(69))/6 ,x=(9+sqrt(69))/6
Find the zeros of -3x^2+9x=1
The zeros of -3x^2+9x=1 are x=(9-sqrt(69))/6 ,x=(9+sqrt(69))/6