What are the solutions to the equation 3x(2x-1)=6 ?

The solutions to the equation 3x(2x-1)=6 are x=(1+sqrt(17))/4 ,x=(1-sqrt(17))/4

Find the zeros of 3x(2x-1)=6

The zeros of 3x(2x-1)=6 are x=(1+sqrt(17))/4 ,x=(1-sqrt(17))/4

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3 x (2 x - 1) = 6

x = \frac{1 + 17}{4}, x = \frac{1 - 17}{4}

Decimal Notation

x = 1.28077 \dots, x = - 0.78077 \dots

Solution steps

3 x (2 x - 1) = 6

Expand

3 x (2 x - 1) : 6 x^{2} - 3 x

6 x^{2} - 3 x = 6

Move

6

to the left side

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

Solve with the quadratic formula

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

(- 3)^{2} - 4 \cdot 6 (- 6) = 317

x_{1, 2} = \frac{- ( - 3 ) \pm 3 17}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 3 17}{2 \cdot 6}, x_{2} = \frac{- ( - 3 ) - 3 17}{2 \cdot 6}

x = \frac{- ( - 3 ) + 3 17}{2 \cdot 6} : \frac{1 + 17}{4}

x = \frac{- ( - 3 ) - 3 17}{2 \cdot 6} : \frac{1 - 17}{4}

The solutions to the quadratic equation are:

x = \frac{1 + 17}{4}, x = \frac{1 - 17}{4}

2 (3 x + 1)^{2} = 0

- 2 x^{2} + 2 x + 40 = 0

- \frac{9.81}{2} t^{2} + 10 t + 45 = 0

2 X + 1 = 8 X^{2}

x, x^{2} - 8 x + b y + 8 = 0

What are the solutions to the equation 3x(2x-1)=6 ?
The solutions to the equation 3x(2x-1)=6 are x=(1+sqrt(17))/4 ,x=(1-sqrt(17))/4
Find the zeros of 3x(2x-1)=6
The zeros of 3x(2x-1)=6 are x=(1+sqrt(17))/4 ,x=(1-sqrt(17))/4