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} - 6 x = 1

Move

1

to the left side

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}

x^{2} + 8 x - 15

3 (x + 2)^{2} - 2 (x - 1) (x + 1) = 11 x + 18

2 x^{2} - 8 x - 5 = 0

x, 4 x^{2} - 21 x - 18 = 0

6 x^{2} - 6 x = 12

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