What are the solutions to the equation -3x^2-3x+1=0 ?

The solutions to the equation -3x^2-3x+1=0 are x=-(3+sqrt(21))/6 ,x=(sqrt(21)-3)/6

Find the zeros of -3x^2-3x+1=0

The zeros of -3x^2-3x+1=0 are x=-(3+sqrt(21))/6 ,x=(sqrt(21)-3)/6

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

x = - \frac{3 + 21}{6}, x = \frac{21 - 3}{6}

Decimal Notation

x = - 1.26376 \dots, x = 0.26376 \dots

Solution steps

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

Solve with the quadratic formula

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

(- 3)^{2} - 4 (- 3) \cdot 1 = 21

x_{1, 2} = \frac{- ( - 3 ) \pm 21}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 21}{2 ( - 3 )}, x_{2} = \frac{- ( - 3 ) - 21}{2 ( - 3 )}

x = \frac{- ( - 3 ) + 21}{2 ( - 3 )} : - \frac{3 + 21}{6}

x = \frac{- ( - 3 ) - 21}{2 ( - 3 )} : \frac{21 - 3}{6}

The solutions to the quadratic equation are:

x = - \frac{3 + 21}{6}, x = \frac{21 - 3}{6}

1 0^{2} + b^{2} = 1 3^{2}

2 x^{2} - 16 x + 8 = 0

x^{2} - 288 x + 1136 = 0

250 = - 0.01 x^{2} + 50 x - 300

3 x^{2} + 22 x + 15 = 0

What are the solutions to the equation -3x^2-3x+1=0 ?
The solutions to the equation -3x^2-3x+1=0 are x=-(3+sqrt(21))/6 ,x=(sqrt(21)-3)/6
Find the zeros of -3x^2-3x+1=0
The zeros of -3x^2-3x+1=0 are x=-(3+sqrt(21))/6 ,x=(sqrt(21)-3)/6