What are the solutions to the equation 3x^2+(3x)/2 = x/3-x+37/3+x^2 ?

The solutions to the equation 3x^2+(3x)/2 = x/3-x+37/3+x^2 are x=-37/12 ,x=2

Find the zeros of 3x^2+(3x)/2 = x/3-x+37/3+x^2

The zeros of 3x^2+(3x)/2 = x/3-x+37/3+x^2 are x=-37/12 ,x=2

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3 x^{2} + \frac{3 x}{2} = \frac{x}{3} - x + \frac{37}{3} + x^{2}

x = - \frac{37}{12}, x = 2

Decimal Notation

x = - 3.08333 \dots, x = 2

Solution steps

3 x^{2} + \frac{3 x}{2} = \frac{x}{3} - x + \frac{37}{3} + x^{2}

Find Least Common Multiplier of

2, 3 : 6

Multiply by LCM=

6

3 x^{2} \cdot 6 + \frac{3 x}{2} \cdot 6 = \frac{x}{3} \cdot 6 - x \cdot 6 + \frac{37}{3} \cdot 6 + x^{2} \cdot 6

Simplify

18 x^{2} + 9 x = 2 x - 6 x + 74 + 6 x^{2}

18 x^{2} + 9 x = - 4 x + 74 + 6 x^{2}

Switch sides

- 4 x + 74 + 6 x^{2} = 18 x^{2} + 9 x

Move

9 x

to the left side

6 x^{2} - 13 x + 74 = 18 x^{2}

Move

18 x^{2}

to the left side

- 12 x^{2} - 13 x + 74 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 13 ) \pm ( - 13 ) ^{2} - 4 ( - 12 ) \cdot 74}{2 ( - 12 )}

(- 13)^{2} - 4 (- 12) \cdot 74 = 61

x_{1, 2} = \frac{- ( - 13 ) \pm 61}{2 ( - 12 )}

Separate the solutions

x_{1} = \frac{- ( - 13 ) + 61}{2 ( - 12 )}, x_{2} = \frac{- ( - 13 ) - 61}{2 ( - 12 )}

x = \frac{- ( - 13 ) + 61}{2 ( - 12 )} : - \frac{37}{12}

x = \frac{- ( - 13 ) - 61}{2 ( - 12 )} : 2

The solutions to the quadratic equation are:

x = - \frac{37}{12}, x = 2

- 8 = 8 (- 3 + a)

15 h + 30 < 10 h - 45

∣ 3 x + 4 ∣ = ∣ 5 x - 3 ∣

2000

What are the solutions to the equation 3x^2+(3x)/2 = x/3-x+37/3+x^2 ?
The solutions to the equation 3x^2+(3x)/2 = x/3-x+37/3+x^2 are x=-37/12 ,x=2
Find the zeros of 3x^2+(3x)/2 = x/3-x+37/3+x^2
The zeros of 3x^2+(3x)/2 = x/3-x+37/3+x^2 are x=-37/12 ,x=2