What are the solutions to the equation 1/4 m^2+3/5 m=-1/4 ?

The solutions to the equation 1/4 m^2+3/5 m=-1/4 are m=(-6+sqrt(11))/5 ,m=-(6+sqrt(11))/5

Find the zeros of 1/4 m^2+3/5 m=-1/4

The zeros of 1/4 m^2+3/5 m=-1/4 are m=(-6+sqrt(11))/5 ,m=-(6+sqrt(11))/5

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\frac{1}{4} m^{2} + \frac{3}{5} m = - \frac{1}{4}

m = \frac{- 6 + 11}{5}, m = - \frac{6 + 11}{5}

Decimal Notation

m = - 0.53667 \dots, m = - 1.86332 \dots

Solution steps

\frac{1}{4} m^{2} + \frac{3}{5} m = - \frac{1}{4}

Find Least Common Multiplier of

4, 5 : 20

Multiply by LCM=

20

\frac{1}{4} m^{2} \cdot 20 + \frac{3}{5} m \cdot 20 = - \frac{1}{4} \cdot 20

Simplify

5 m^{2} + 12 m = - 5

Move

5

to the left side

5 m^{2} + 12 m + 5 = 0

Solve with the quadratic formula

m_{1, 2} = \frac{- 12 \pm 1 2 ^{2} - 4 \cdot 5 \cdot 5}{2 \cdot 5}

1 2^{2} - 4 \cdot 5 \cdot 5 = 211

m_{1, 2} = \frac{- 12 \pm 2 11}{2 \cdot 5}

Separate the solutions

m_{1} = \frac{- 12 + 2 11}{2 \cdot 5}, m_{2} = \frac{- 12 - 2 11}{2 \cdot 5}

m = \frac{- 12 + 2 11}{2 \cdot 5} : \frac{- 6 + 11}{5}

m = \frac{- 12 - 2 11}{2 \cdot 5} : - \frac{6 + 11}{5}

The solutions to the quadratic equation are:

m = \frac{- 6 + 11}{5}, m = - \frac{6 + 11}{5}

0 = - \frac{2}{3} (x - 1) (x + 3)

7 x^{2} = 22 x - 3

(y - 5)^{2} = 0

4 x^{2} + 8 x - 20 = 0

x, (x + y)^{2} = 9

What are the solutions to the equation 1/4 m^2+3/5 m=-1/4 ?
The solutions to the equation 1/4 m^2+3/5 m=-1/4 are m=(-6+sqrt(11))/5 ,m=-(6+sqrt(11))/5
Find the zeros of 1/4 m^2+3/5 m=-1/4
The zeros of 1/4 m^2+3/5 m=-1/4 are m=(-6+sqrt(11))/5 ,m=-(6+sqrt(11))/5