What are the solutions to the equation 0=3x^2-12x+11 ?

The solutions to the equation 0=3x^2-12x+11 are x=(6+sqrt(3))/3 ,x=(6-sqrt(3))/3

Find the zeros of 0=3x^2-12x+11

The zeros of 0=3x^2-12x+11 are x=(6+sqrt(3))/3 ,x=(6-sqrt(3))/3

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0 = 3 x^{2} - 12 x + 11

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

Decimal Notation

x = 2.57735 \dots, x = 1.42264 \dots

Solution steps

0 = 3 x^{2} - 12 x + 11

Switch sides

3 x^{2} - 12 x + 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 3 \cdot 11}{2 \cdot 3}

(- 12)^{2} - 4 \cdot 3 \cdot 11 = 23

x_{1, 2} = \frac{- ( - 12 ) \pm 2 3}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 2 3}{2 \cdot 3}, x_{2} = \frac{- ( - 12 ) - 2 3}{2 \cdot 3}

x = \frac{- ( - 12 ) + 2 3}{2 \cdot 3} : \frac{6 + 3}{3}

x = \frac{- ( - 12 ) - 2 3}{2 \cdot 3} : \frac{6 - 3}{3}

The solutions to the quadratic equation are:

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

x^{2} + 6 x - 15 = 0

x - 3 \geq 4

499

\frac{2}{6 + 5 i}

x^{2} - 4 = - 3

What are the solutions to the equation 0=3x^2-12x+11 ?
The solutions to the equation 0=3x^2-12x+11 are x=(6+sqrt(3))/3 ,x=(6-sqrt(3))/3
Find the zeros of 0=3x^2-12x+11
The zeros of 0=3x^2-12x+11 are x=(6+sqrt(3))/3 ,x=(6-sqrt(3))/3