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

The solutions to the equation 1/4 q^2+3/4 q=-1/3 are q=(-9+sqrt(33))/6 ,q=(-9-sqrt(33))/6

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

The zeros of 1/4 q^2+3/4 q=-1/3 are q=(-9+sqrt(33))/6 ,q=(-9-sqrt(33))/6

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

q = \frac{- 9 + 33}{6}, q = \frac{- 9 - 33}{6}

Decimal Notation

q = - 0.54257 \dots, q = - 2.45742 \dots

Solution steps

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

Find Least Common Multiplier of

4, 3 : 12

Multiply by LCM=

12

\frac{1}{4} q^{2} \cdot 12 + \frac{3}{4} q \cdot 12 = - \frac{1}{3} \cdot 12

Simplify

3 q^{2} + 9 q = - 4

Move

4

to the left side

3 q^{2} + 9 q + 4 = 0

Solve with the quadratic formula

q_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 \cdot 3 \cdot 4}{2 \cdot 3}

9^{2} - 4 \cdot 3 \cdot 4 = 33

q_{1, 2} = \frac{- 9 \pm 33}{2 \cdot 3}

Separate the solutions

q_{1} = \frac{- 9 + 33}{2 \cdot 3}, q_{2} = \frac{- 9 - 33}{2 \cdot 3}

q = \frac{- 9 + 33}{2 \cdot 3} : \frac{- 9 + 33}{6}

q = \frac{- 9 - 33}{2 \cdot 3} : \frac{- 9 - 33}{6}

The solutions to the quadratic equation are:

q = \frac{- 9 + 33}{6}, q = \frac{- 9 - 33}{6}

x^{2} + 3 x - 16 < 0

7 ∣ d ∣ \geq 14

(4 + i 4) + (9 - i 9)

(- 16)^{- \frac{3}{2}}

7 \geq \frac{3 - 4 x}{3}

What are the solutions to the equation 1/4 q^2+3/4 q=-1/3 ?
The solutions to the equation 1/4 q^2+3/4 q=-1/3 are q=(-9+sqrt(33))/6 ,q=(-9-sqrt(33))/6
Find the zeros of 1/4 q^2+3/4 q=-1/3
The zeros of 1/4 q^2+3/4 q=-1/3 are q=(-9+sqrt(33))/6 ,q=(-9-sqrt(33))/6