What are the solutions to the equation 3x^2-12x-5=0 ?

The solutions to the equation 3x^2-12x-5=0 are x=(6+sqrt(51))/3 ,x=(6-sqrt(51))/3

Find the zeros of 3x^2-12x-5=0

The zeros of 3x^2-12x-5=0 are x=(6+sqrt(51))/3 ,x=(6-sqrt(51))/3

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3 x^{2} - 12 x - 5 = 0

x = \frac{6 + 51}{3}, x = \frac{6 - 51}{3}

Decimal Notation

x = 4.38047 \dots, x = - 0.38047 \dots

Solution steps

3 x^{2} - 12 x - 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 3 ( - 5 )}{2 \cdot 3}

(- 12)^{2} - 4 \cdot 3 (- 5) = 251

x_{1, 2} = \frac{- ( - 12 ) \pm 2 51}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 2 51}{2 \cdot 3}, x_{2} = \frac{- ( - 12 ) - 2 51}{2 \cdot 3}

x = \frac{- ( - 12 ) + 2 51}{2 \cdot 3} : \frac{6 + 51}{3}

x = \frac{- ( - 12 ) - 2 51}{2 \cdot 3} : \frac{6 - 51}{3}

The solutions to the quadratic equation are:

x = \frac{6 + 51}{3}, x = \frac{6 - 51}{3}

(x - 8) (x - 2) = - 9

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

3 x^{2} - 12 x - 4 = 0

x^{2} - 6 = 138

s^{2} + 3.91 s + 14.846 = 0

What are the solutions to the equation 3x^2-12x-5=0 ?
The solutions to the equation 3x^2-12x-5=0 are x=(6+sqrt(51))/3 ,x=(6-sqrt(51))/3
Find the zeros of 3x^2-12x-5=0
The zeros of 3x^2-12x-5=0 are x=(6+sqrt(51))/3 ,x=(6-sqrt(51))/3