What are the solutions to the equation 3x(x-4)=6 ?

The solutions to the equation 3x(x-4)=6 are x=2+sqrt(6),x=2-sqrt(6)

Find the zeros of 3x(x-4)=6

The zeros of 3x(x-4)=6 are x=2+sqrt(6),x=2-sqrt(6)

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3 x (x - 4) = 6

x = 2 + 6, x = 2 - 6

Decimal Notation

x = 4.44948 \dots, x = - 0.44948 \dots

Solution steps

3 x (x - 4) = 6

Expand

3 x (x - 4) : 3 x^{2} - 12 x

3 x^{2} - 12 x = 6

Move

6

to the left side

3 x^{2} - 12 x - 6 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 3 ( - 6 )}{2 \cdot 3}

(- 12)^{2} - 4 \cdot 3 (- 6) = 66

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = 2 + 6, x = 2 - 6

6 x^{2} + 24 x = - 10

x (6 x + 7) = 3

x^{2} + 32 x + 116 = 12 x

2 x^{2} + 2 x + 32 = 0

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

What are the solutions to the equation 3x(x-4)=6 ?
The solutions to the equation 3x(x-4)=6 are x=2+sqrt(6),x=2-sqrt(6)
Find the zeros of 3x(x-4)=6
The zeros of 3x(x-4)=6 are x=2+sqrt(6),x=2-sqrt(6)