What are the solutions to the equation 14m^2+1=6m^2+7m ?

The solutions to the equation 14m^2+1=6m^2+7m are m=(7+sqrt(17))/(16),m=(7-sqrt(17))/(16)

Find the zeros of 14m^2+1=6m^2+7m

The zeros of 14m^2+1=6m^2+7m are m=(7+sqrt(17))/(16),m=(7-sqrt(17))/(16)

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14 m^{2} + 1 = 6 m^{2} + 7 m

m = \frac{7 + 17}{16}, m = \frac{7 - 17}{16}

Decimal Notation

m = 0.69519 \dots, m = 0.17980 \dots

Solution steps

14 m^{2} + 1 = 6 m^{2} + 7 m

Move

7 m

to the left side

14 m^{2} + 1 - 7 m = 6 m^{2}

Move

6 m^{2}

to the left side

8 m^{2} - 7 m + 1 = 0

Solve with the quadratic formula

m_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot 8 \cdot 1}{2 \cdot 8}

(- 7)^{2} - 4 \cdot 8 \cdot 1 = 17

m_{1, 2} = \frac{- ( - 7 ) \pm 17}{2 \cdot 8}

Separate the solutions

m_{1} = \frac{- ( - 7 ) + 17}{2 \cdot 8}, m_{2} = \frac{- ( - 7 ) - 17}{2 \cdot 8}

m = \frac{- ( - 7 ) + 17}{2 \cdot 8} : \frac{7 + 17}{16}

m = \frac{- ( - 7 ) - 17}{2 \cdot 8} : \frac{7 - 17}{16}

The solutions to the quadratic equation are:

m = \frac{7 + 17}{16}, m = \frac{7 - 17}{16}

3 x^{2} + 12 x + 19 = 7

\frac{x}{100} = \frac{5089.3801}{9025.7957}

r^{2} + 4 r + 20 = 0

6 \leq - 4 x + 6 < 2

2 (x - 4) = 3 (1 + x)

What are the solutions to the equation 14m^2+1=6m^2+7m ?
The solutions to the equation 14m^2+1=6m^2+7m are m=(7+sqrt(17))/(16),m=(7-sqrt(17))/(16)
Find the zeros of 14m^2+1=6m^2+7m
The zeros of 14m^2+1=6m^2+7m are m=(7+sqrt(17))/(16),m=(7-sqrt(17))/(16)