What are the solutions to the equation 6x^2-6x-11=0 ?

The solutions to the equation 6x^2-6x-11=0 are x=(3+5sqrt(3))/6 ,x=(3-5sqrt(3))/6

Find the zeros of 6x^2-6x-11=0

The zeros of 6x^2-6x-11=0 are x=(3+5sqrt(3))/6 ,x=(3-5sqrt(3))/6

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6 x^{2} - 6 x - 11 = 0

x = \frac{3 + 5 3}{6}, x = \frac{3 - 5 3}{6}

Decimal Notation

x = 1.94337 \dots, x = - 0.94337 \dots

Solution steps

6 x^{2} - 6 x - 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 6 ( - 11 )}{2 \cdot 6}

(- 6)^{2} - 4 \cdot 6 (- 11) = 103

x_{1, 2} = \frac{- ( - 6 ) \pm 10 3}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 10 3}{2 \cdot 6}, x_{2} = \frac{- ( - 6 ) - 10 3}{2 \cdot 6}

x = \frac{- ( - 6 ) + 10 3}{2 \cdot 6} : \frac{3 + 5 3}{6}

x = \frac{- ( - 6 ) - 10 3}{2 \cdot 6} : \frac{3 - 5 3}{6}

The solutions to the quadratic equation are:

x = \frac{3 + 5 3}{6}, x = \frac{3 - 5 3}{6}

x, y = - 6 x^{2} + 42 x - 60

- 3 x^{2} + 2 x - 7 = 0

a, (x^{2} + y^{2})^{2} = 2 a^{2} x y

x^{2} + 28 x = 0

3 x^{2} + 10 + 15 x + 20 = 180

What are the solutions to the equation 6x^2-6x-11=0 ?
The solutions to the equation 6x^2-6x-11=0 are x=(3+5sqrt(3))/6 ,x=(3-5sqrt(3))/6
Find the zeros of 6x^2-6x-11=0
The zeros of 6x^2-6x-11=0 are x=(3+5sqrt(3))/6 ,x=(3-5sqrt(3))/6