What are the solutions to the equation 12=3x^2-18x ?

The solutions to the equation 12=3x^2-18x are x=3+sqrt(13),x=3-sqrt(13)

Find the zeros of 12=3x^2-18x

The zeros of 12=3x^2-18x are x=3+sqrt(13),x=3-sqrt(13)

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12 = 3 x^{2} - 18 x

x = 3 + 13, x = 3 - 13

Decimal Notation

x = 6.60555 \dots, x = - 0.60555 \dots

Solution steps

12 = 3 x^{2} - 18 x

Switch sides

3 x^{2} - 18 x = 12

Move

12

to the left side

3 x^{2} - 18 x - 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 3 ( - 12 )}{2 \cdot 3}

(- 18)^{2} - 4 \cdot 3 (- 12) = 613

x_{1, 2} = \frac{- ( - 18 ) \pm 6 13}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 18 ) + 6 13}{2 \cdot 3}, x_{2} = \frac{- ( - 18 ) - 6 13}{2 \cdot 3}

x = \frac{- ( - 18 ) + 6 13}{2 \cdot 3} : 3 + 13

x = \frac{- ( - 18 ) - 6 13}{2 \cdot 3} : 3 - 13

The solutions to the quadratic equation are:

x = 3 + 13, x = 3 - 13

(- \frac{13}{3} x)^{2} + (- \frac{2}{3} x)^{2} + x^{2} = 1

2 x^{2} + 6 x - 196 = 0

4 m^{2} - 8 m + 9 = 0

26 x^{2} + 41 x + 20 = 6 x^{2}

- 0.00015 x^{2} - 0.001652 x + 0.0153 = 0

What are the solutions to the equation 12=3x^2-18x ?
The solutions to the equation 12=3x^2-18x are x=3+sqrt(13),x=3-sqrt(13)
Find the zeros of 12=3x^2-18x
The zeros of 12=3x^2-18x are x=3+sqrt(13),x=3-sqrt(13)