What are the solutions to the equation 6x-2/3 x^2=3 ?

The solutions to the equation 6x-2/3 x^2=3 are x=(3(3-sqrt(7)))/2 ,x=(3(3+sqrt(7)))/2

Find the zeros of 6x-2/3 x^2=3

The zeros of 6x-2/3 x^2=3 are x=(3(3-sqrt(7)))/2 ,x=(3(3+sqrt(7)))/2

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6 x - \frac{2}{3} x^{2} = 3

x = \frac{3 ( 3 - 7 )}{2}, x = \frac{3 ( 3 + 7 )}{2}

Decimal Notation

x = 0.53137 \dots, x = 8.46862 \dots

Solution steps

6 x - \frac{2}{3} x^{2} = 3

Multiply both sides by

3

18 x - 2 x^{2} = 9

Move

9

to the left side

18 x - 2 x^{2} - 9 = 0

Write in the standard form

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

- 2 x^{2} + 18 x - 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 18 \pm 1 8 ^{2} - 4 ( - 2 ) ( - 9 )}{2 ( - 2 )}

1 8^{2} - 4 (- 2) (- 9) = 67

x_{1, 2} = \frac{- 18 \pm 6 7}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 18 + 6 7}{2 ( - 2 )}, x_{2} = \frac{- 18 - 6 7}{2 ( - 2 )}

x = \frac{- 18 + 6 7}{2 ( - 2 )} : \frac{3 ( 3 - 7 )}{2}

x = \frac{- 18 - 6 7}{2 ( - 2 )} : \frac{3 ( 3 + 7 )}{2}

The solutions to the quadratic equation are:

x = \frac{3 ( 3 - 7 )}{2}, x = \frac{3 ( 3 + 7 )}{2}

x^{2} - 3 x - 18 \leq 0

(e^{2})^{3}

11 x - 12 = 3 + 4 x

49 x^{2} - 56 x + 16 = 0

What are the solutions to the equation 6x-2/3 x^2=3 ?
The solutions to the equation 6x-2/3 x^2=3 are x=(3(3-sqrt(7)))/2 ,x=(3(3+sqrt(7)))/2
Find the zeros of 6x-2/3 x^2=3
The zeros of 6x-2/3 x^2=3 are x=(3(3-sqrt(7)))/2 ,x=(3(3+sqrt(7)))/2