What are the solutions to the equation 1/3 u^2+2/3 u=-1/12 ?

The solutions to the equation 1/3 u^2+2/3 u=-1/12 are u=(-2+sqrt(3))/2 ,u=-(2+sqrt(3))/2

Find the zeros of 1/3 u^2+2/3 u=-1/12

The zeros of 1/3 u^2+2/3 u=-1/12 are u=(-2+sqrt(3))/2 ,u=-(2+sqrt(3))/2

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\frac{1}{3} u^{2} + \frac{2}{3} u = - \frac{1}{12}

u = \frac{- 2 + 3}{2}, u = - \frac{2 + 3}{2}

Decimal Notation

u = - 0.13397 \dots, u = - 1.86602 \dots

Solution steps

\frac{1}{3} u^{2} + \frac{2}{3} u = - \frac{1}{12}

Find Least Common Multiplier of

3, 12 : 12

Multiply by LCM=

12

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

Simplify

4 u^{2} + 8 u = - 1

Move

1

to the left side

4 u^{2} + 8 u + 1 = 0

Solve with the quadratic formula

u_{1, 2} = \frac{- 8 \pm 8 ^{2} - 4 \cdot 4 \cdot 1}{2 \cdot 4}

8^{2} - 4 \cdot 4 \cdot 1 = 43

u_{1, 2} = \frac{- 8 \pm 4 3}{2 \cdot 4}

Separate the solutions

u_{1} = \frac{- 8 + 4 3}{2 \cdot 4}, u_{2} = \frac{- 8 - 4 3}{2 \cdot 4}

u = \frac{- 8 + 4 3}{2 \cdot 4} : \frac{- 2 + 3}{2}

u = \frac{- 8 - 4 3}{2 \cdot 4} : - \frac{2 + 3}{2}

The solutions to the quadratic equation are:

u = \frac{- 2 + 3}{2}, u = - \frac{2 + 3}{2}

(5 - 4 i)^{2}

\frac{3 x + 2}{x ^{3} - x ^{2}} > 0

- \frac{1}{2} - \frac{1}{5}

(\frac{5 x ^{3} y}{20 x y ^{5}})^{4}

x^{3} - 3 x - 18

What are the solutions to the equation 1/3 u^2+2/3 u=-1/12 ?
The solutions to the equation 1/3 u^2+2/3 u=-1/12 are u=(-2+sqrt(3))/2 ,u=-(2+sqrt(3))/2
Find the zeros of 1/3 u^2+2/3 u=-1/12
The zeros of 1/3 u^2+2/3 u=-1/12 are u=(-2+sqrt(3))/2 ,u=-(2+sqrt(3))/2