What are the solutions to the equation 3x^2-3/2 x= 1/3 ?

The solutions to the equation 3x^2-3/2 x= 1/3 are x= 2/3 ,x=-1/6

Find the zeros of 3x^2-3/2 x= 1/3

The zeros of 3x^2-3/2 x= 1/3 are x= 2/3 ,x=-1/6

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3 x^{2} - \frac{3}{2} x = \frac{1}{3}

x = \frac{2}{3}, x = - \frac{1}{6}

Decimal Notation

x = 0.66666 \dots, x = - 0.16666 \dots

Solution steps

3 x^{2} - \frac{3}{2} x = \frac{1}{3}

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

3 x^{2} \cdot 6 - \frac{3}{2} x \cdot 6 = \frac{1}{3} \cdot 6

Simplify

18 x^{2} - 9 x = 2

Move

2

to the left side

18 x^{2} - 9 x - 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 18 ( - 2 )}{2 \cdot 18}

(- 9)^{2} - 4 \cdot 18 (- 2) = 15

x_{1, 2} = \frac{- ( - 9 ) \pm 15}{2 \cdot 18}

Separate the solutions

x_{1} = \frac{- ( - 9 ) + 15}{2 \cdot 18}, x_{2} = \frac{- ( - 9 ) - 15}{2 \cdot 18}

x = \frac{- ( - 9 ) + 15}{2 \cdot 18} : \frac{2}{3}

x = \frac{- ( - 9 ) - 15}{2 \cdot 18} : - \frac{1}{6}

The solutions to the quadratic equation are:

x = \frac{2}{3}, x = - \frac{1}{6}

(x - 7) (x - 1) = 0

8 x^{2} = 14 x - 3

x^{2} + 9 + 8 x = 0

4 x^{2} - 45 x - 269 = 7 x^{2} - 3 x + 7

2 x^{2} + 48 = - 20 x

What are the solutions to the equation 3x^2-3/2 x= 1/3 ?
The solutions to the equation 3x^2-3/2 x= 1/3 are x= 2/3 ,x=-1/6
Find the zeros of 3x^2-3/2 x= 1/3
The zeros of 3x^2-3/2 x= 1/3 are x= 2/3 ,x=-1/6