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

The solutions to the equation 3x^2-12x-3=0 are x=2+sqrt(5),x=2-sqrt(5)

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

The zeros of 3x^2-12x-3=0 are x=2+sqrt(5),x=2-sqrt(5)

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

x = 2 + 5, x = 2 - 5

Decimal Notation

x = 4.23606 \dots, x = - 0.23606 \dots

Solution steps

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

Solve with the quadratic formula

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

(- 12)^{2} - 4 \cdot 3 (- 3) = 65

x_{1, 2} = \frac{- ( - 12 ) \pm 6 5}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 6 5}{2 \cdot 3}, x_{2} = \frac{- ( - 12 ) - 6 5}{2 \cdot 3}

x = \frac{- ( - 12 ) + 6 5}{2 \cdot 3} : 2 + 5

x = \frac{- ( - 12 ) - 6 5}{2 \cdot 3} : 2 - 5

The solutions to the quadratic equation are:

x = 2 + 5, x = 2 - 5

- \frac{1}{3} - \frac{1}{2}

- \frac{8 ( 7 + 1 )}{( 7 - 3 ) ^{3}}

\frac{4 ( 3 x - 2 )}{8} = 14

5 (x^{0}) y^{- 1}

n^{2} + 13 n + 36

What are the solutions to the equation 3x^2-12x-3=0 ?
The solutions to the equation 3x^2-12x-3=0 are x=2+sqrt(5),x=2-sqrt(5)
Find the zeros of 3x^2-12x-3=0
The zeros of 3x^2-12x-3=0 are x=2+sqrt(5),x=2-sqrt(5)