What are the solutions to the equation 3x^2-x=11 ?

The solutions to the equation 3x^2-x=11 are x=(1+sqrt(133))/6 ,x=(1-sqrt(133))/6

Find the zeros of 3x^2-x=11

The zeros of 3x^2-x=11 are x=(1+sqrt(133))/6 ,x=(1-sqrt(133))/6

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3 x^{2} - x = 11

x = \frac{1 + 133}{6}, x = \frac{1 - 133}{6}

Decimal Notation

x = 2.08876 \dots, x = - 1.75542 \dots

Solution steps

3 x^{2} - x = 11

Move

11

to the left side

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

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 3 ( - 11 )}{2 \cdot 3}

(- 1)^{2} - 4 \cdot 3 (- 11) = 133

x_{1, 2} = \frac{- ( - 1 ) \pm 133}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 1 ) + 133}{2 \cdot 3}, x_{2} = \frac{- ( - 1 ) - 133}{2 \cdot 3}

x = \frac{- ( - 1 ) + 133}{2 \cdot 3} : \frac{1 + 133}{6}

x = \frac{- ( - 1 ) - 133}{2 \cdot 3} : \frac{1 - 133}{6}

The solutions to the quadratic equation are:

x = \frac{1 + 133}{6}, x = \frac{1 - 133}{6}

x^{2} - 18 x + 24 = - 7 x

x^{2} + 2 x - 68 = 2 x - 4

4 z^{2} - 2 z = 12

x^{2} - 38 = - 3 x - 10

x^{2} - 20 x - 91 = 0

What are the solutions to the equation 3x^2-x=11 ?
The solutions to the equation 3x^2-x=11 are x=(1+sqrt(133))/6 ,x=(1-sqrt(133))/6
Find the zeros of 3x^2-x=11
The zeros of 3x^2-x=11 are x=(1+sqrt(133))/6 ,x=(1-sqrt(133))/6