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

The solutions to the equation 1/3 x^2-2x-2=0 are x=3+sqrt(15),x=3-sqrt(15)

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

The zeros of 1/3 x^2-2x-2=0 are x=3+sqrt(15),x=3-sqrt(15)

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\frac{1}{3} x^{2} - 2 x - 2 = 0

x = 3 + 15, x = 3 - 15

Decimal Notation

x = 6.87298 \dots, x = - 0.87298 \dots

Solution steps

\frac{1}{3} x^{2} - 2 x - 2 = 0

Multiply both sides by

3

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

Solve with the quadratic formula

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

(- 6)^{2} - 4 \cdot 1 \cdot (- 6) = 215

x_{1, 2} = \frac{- ( - 6 ) \pm 2 15}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 15}{2 \cdot 1}, x_{2} = \frac{- ( - 6 ) - 2 15}{2 \cdot 1}

x = \frac{- ( - 6 ) + 2 15}{2 \cdot 1} : 3 + 15

x = \frac{- ( - 6 ) - 2 15}{2 \cdot 1} : 3 - 15

The solutions to the quadratic equation are:

x = 3 + 15, x = 3 - 15

\frac{x ^{2}}{9} = \frac{1}{3}

x^{2} + 20 x + 5 = 0

(x + 1)^{2} - 4 x = 1

124 = - 16 t^{2} + 100 t + 10

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

What are the solutions to the equation 1/3 x^2-2x-2=0 ?
The solutions to the equation 1/3 x^2-2x-2=0 are x=3+sqrt(15),x=3-sqrt(15)
Find the zeros of 1/3 x^2-2x-2=0
The zeros of 1/3 x^2-2x-2=0 are x=3+sqrt(15),x=3-sqrt(15)