What are the solutions to the equation 3x(x-3)=7 ?

The solutions to the equation 3x(x-3)=7 are x=(9+sqrt(165))/6 ,x=(9-sqrt(165))/6

Find the zeros of 3x(x-3)=7

The zeros of 3x(x-3)=7 are x=(9+sqrt(165))/6 ,x=(9-sqrt(165))/6

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3 x (x - 3) = 7

x = \frac{9 + 165}{6}, x = \frac{9 - 165}{6}

Decimal Notation

x = 3.64087 \dots, x = - 0.64087 \dots

Solution steps

3 x (x - 3) = 7

Expand

3 x (x - 3) : 3 x^{2} - 9 x

3 x^{2} - 9 x = 7

Move

7

to the left side

3 x^{2} - 9 x - 7 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 3 ( - 7 )}{2 \cdot 3}

(- 9)^{2} - 4 \cdot 3 (- 7) = 165

x_{1, 2} = \frac{- ( - 9 ) \pm 165}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 9 ) + 165}{2 \cdot 3}, x_{2} = \frac{- ( - 9 ) - 165}{2 \cdot 3}

x = \frac{- ( - 9 ) + 165}{2 \cdot 3} : \frac{9 + 165}{6}

x = \frac{- ( - 9 ) - 165}{2 \cdot 3} : \frac{9 - 165}{6}

The solutions to the quadratic equation are:

x = \frac{9 + 165}{6}, x = \frac{9 - 165}{6}

3 x (x - 3) = 0

4 x^{2} - 64 = 0

- x^{2} + 16 x + 0 = 0

(x - a)^{2} + x^{2} = 2 a^{2}

4 x^{2} + x - 14 = 0

What are the solutions to the equation 3x(x-3)=7 ?
The solutions to the equation 3x(x-3)=7 are x=(9+sqrt(165))/6 ,x=(9-sqrt(165))/6
Find the zeros of 3x(x-3)=7
The zeros of 3x(x-3)=7 are x=(9+sqrt(165))/6 ,x=(9-sqrt(165))/6