What are the solutions to the equation 2m^2-6m+10=3m-m^2-6 ?

The solutions to the equation 2m^2-6m+10=3m-m^2-6 are m= 3/2+i(sqrt(111))/6 ,m= 3/2-i(sqrt(111))/6

Find the zeros of 2m^2-6m+10=3m-m^2-6

The zeros of 2m^2-6m+10=3m-m^2-6 are m= 3/2+i(sqrt(111))/6 ,m= 3/2-i(sqrt(111))/6

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2 m^{2} - 6 m + 10 = 3 m - m^{2} - 6

m = \frac{3}{2} + i \frac{111}{6}, m = \frac{3}{2} - i \frac{111}{6}

Solution steps

2 m^{2} - 6 m + 10 = 3 m - m^{2} - 6

Move

6

to the left side

2 m^{2} - 6 m + 16 = 3 m - m^{2}

Move

m^{2}

to the left side

3 m^{2} - 6 m + 16 = 3 m

Move

3 m

to the left side

3 m^{2} - 9 m + 16 = 0

Solve with the quadratic formula

m_{1, 2} = \frac{- ( - 9 ) \pm ( - 9 ) ^{2} - 4 \cdot 3 \cdot 16}{2 \cdot 3}

Simplify

(- 9)^{2} - 4 \cdot 3 \cdot 16 : 111 i

m_{1, 2} = \frac{- ( - 9 ) \pm 111 i}{2 \cdot 3}

Separate the solutions

m_{1} = \frac{- ( - 9 ) + 111 i}{2 \cdot 3}, m_{2} = \frac{- ( - 9 ) - 111 i}{2 \cdot 3}

m = \frac{- ( - 9 ) + 111 i}{2 \cdot 3} : \frac{3}{2} + i \frac{111}{6}

m = \frac{- ( - 9 ) - 111 i}{2 \cdot 3} : \frac{3}{2} - i \frac{111}{6}

The solutions to the quadratic equation are:

m = \frac{3}{2} + i \frac{111}{6}, m = \frac{3}{2} - i \frac{111}{6}

32 x^{2} - 8 x + 1 = 0

2 (x - 2) = 4 x - 3 (x + 2)^{2}

0 = 3 x^{2} + 22 x - 16

3 e x^{2} - 4 e = 2 x

5 x^{2} + 2 x - 3 + 9 x = 0

What are the solutions to the equation 2m^2-6m+10=3m-m^2-6 ?
The solutions to the equation 2m^2-6m+10=3m-m^2-6 are m= 3/2+i(sqrt(111))/6 ,m= 3/2-i(sqrt(111))/6
Find the zeros of 2m^2-6m+10=3m-m^2-6
The zeros of 2m^2-6m+10=3m-m^2-6 are m= 3/2+i(sqrt(111))/6 ,m= 3/2-i(sqrt(111))/6