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

The solutions to the equation 3x^2-3=3x are x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

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

The zeros of 3x^2-3=3x are x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2

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3 x^{2} - 3 = 3 x

x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

Decimal Notation

x = 1.61803 \dots, x = - 0.61803 \dots

Solution steps

3 x^{2} - 3 = 3 x

Move

3 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

(- 3)^{2} - 4 \cdot 3 (- 3) = 35

x_{1, 2} = \frac{- ( - 3 ) \pm 3 5}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 3 5}{2 \cdot 3}, x_{2} = \frac{- ( - 3 ) - 3 5}{2 \cdot 3}

x = \frac{- ( - 3 ) + 3 5}{2 \cdot 3} : \frac{1 + 5}{2}

x = \frac{- ( - 3 ) - 3 5}{2 \cdot 3} : \frac{1 - 5}{2}

The solutions to the quadratic equation are:

x = \frac{1 + 5}{2}, x = \frac{1 - 5}{2}

5 x^{2} + 50 x + 45 = 0

5 x^{2} = 900

5 x^{2} = 3 x^{2} + 24

5 x^{2} + 8 x = 4

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

What are the solutions to the equation 3x^2-3=3x ?
The solutions to the equation 3x^2-3=3x are x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2
Find the zeros of 3x^2-3=3x
The zeros of 3x^2-3=3x are x=(1+sqrt(5))/2 ,x=(1-sqrt(5))/2