What are the solutions to the equation 3x^2-1=6x ?

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

Find the zeros of 3x^2-1=6x

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

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3 x^{2} - 1 = 6 x

x = \frac{3 + 2 3}{3}, x = \frac{3 - 2 3}{3}

Decimal Notation

x = 2.15470 \dots, x = - 0.15470 \dots

Solution steps

3 x^{2} - 1 = 6 x

Move

6 x

to the left side

3 x^{2} - 1 - 6 x = 0

Write in the standard form

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

3 x^{2} - 6 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 3 ( - 1 )}{2 \cdot 3}

(- 6)^{2} - 4 \cdot 3 (- 1) = 43

x_{1, 2} = \frac{- ( - 6 ) \pm 4 3}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 4 3}{2 \cdot 3}, x_{2} = \frac{- ( - 6 ) - 4 3}{2 \cdot 3}

x = \frac{- ( - 6 ) + 4 3}{2 \cdot 3} : \frac{3 + 2 3}{3}

x = \frac{- ( - 6 ) - 4 3}{2 \cdot 3} : \frac{3 - 2 3}{3}

The solutions to the quadratic equation are:

x = \frac{3 + 2 3}{3}, x = \frac{3 - 2 3}{3}

5 x^{2} + 9 x = 10

a, a^{2} + 6 ab = 16 b^{2}

\frac{3 - x}{1000} = \frac{40 \cdot 10}{2 \cdot 1} (3 - x - 0.7)^{2}

- 5 x^{2} + 40 x - 40 = 0

p^{2} - 3 p - 18 = 0

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