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

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

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

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

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3 x^{2} + 1 = 6 x

x = \frac{3 + 6}{3}, x = \frac{3 - 6}{3}

Decimal

x = 1.81649 \dots, x = 0.18350 \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 \cdot 1}{2 \cdot 3}

(- 6)^{2} - 4 \cdot 3 \cdot 1 = 26

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = \frac{3 + 6}{3}, x = \frac{3 - 6}{3}

2 s^{2} + 12 s = 0

4 x - 9 = x (2 - x)

(x + 2) (x - 2) - 3 x = 0

5 x^{2} + 6 = - 19 b + 2 b^{2}

x^{2} + 18 = 9

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