What are the solutions to the equation 3x(x+6)=2(3x-10) ?

The solutions to the equation 3x(x+6)=2(3x-10) are x=-2+i(2sqrt(6))/3 ,x=-2-i(2sqrt(6))/3

Find the zeros of 3x(x+6)=2(3x-10)

The zeros of 3x(x+6)=2(3x-10) are x=-2+i(2sqrt(6))/3 ,x=-2-i(2sqrt(6))/3

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3 x (x + 6) = 2 (3 x - 10)

x = - 2 + i \frac{2 6}{3}, x = - 2 - i \frac{2 6}{3}

Solution steps

3 x (x + 6) = 2 (3 x - 10)

Expand

3 x (x + 6) : 3 x^{2} + 18 x

Expand

2 (3 x - 10) : 6 x - 20

3 x^{2} + 18 x = 6 x - 20

Move

20

to the left side

3 x^{2} + 18 x + 20 = 6 x

Move

6 x

to the left side

3 x^{2} + 12 x + 20 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 3 \cdot 20}{2 \cdot 3}

Simplify

1 2^{2} - 4 \cdot 3 \cdot 20 : 46 i

x_{1, 2} = \frac{- 12 \pm 4 6 i}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 12 + 4 6 i}{2 \cdot 3}, x_{2} = \frac{- 12 - 4 6 i}{2 \cdot 3}

x = \frac{- 12 + 4 6 i}{2 \cdot 3} : - 2 + i \frac{2 6}{3}

x = \frac{- 12 - 4 6 i}{2 \cdot 3} : - 2 - i \frac{2 6}{3}

The solutions to the quadratic equation are:

x = - 2 + i \frac{2 6}{3}, x = - 2 - i \frac{2 6}{3}

∣ 2 s - 7 ∣ > - 1

3 (x + 2) = 15

2 x^{2} + 4 x + 6 = 0

1.2 (x + 7.5) = 2.5 x - 17

x^{2} = 5 x + 6

What are the solutions to the equation 3x(x+6)=2(3x-10) ?
The solutions to the equation 3x(x+6)=2(3x-10) are x=-2+i(2sqrt(6))/3 ,x=-2-i(2sqrt(6))/3
Find the zeros of 3x(x+6)=2(3x-10)
The zeros of 3x(x+6)=2(3x-10) are x=-2+i(2sqrt(6))/3 ,x=-2-i(2sqrt(6))/3