What are the solutions to the equation (x^2)/3-x=-1/2 ?

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

Find the zeros of (x^2)/3-x=-1/2

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

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\frac{x ^{2}}{3} - x = - \frac{1}{2}

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

Solution steps

\frac{x ^{2}}{3} - x = - \frac{1}{2}

Find Least Common Multiplier of

3, 2 : 6

Multiply by LCM=

6

\frac{x ^{2}}{3} \cdot 6 - x \cdot 6 = - \frac{1}{2} \cdot 6

Simplify

2 x^{2} - 6 x = - 3

Move

3

to the left side

2 x^{2} - 6 x + 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 2 \cdot 3}{2 \cdot 2}

(- 6)^{2} - 4 \cdot 2 \cdot 3 = 23

x_{1, 2} = \frac{- ( - 6 ) \pm 2 3}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 3}{2 \cdot 2}, x_{2} = \frac{- ( - 6 ) - 2 3}{2 \cdot 2}

x = \frac{- ( - 6 ) + 2 3}{2 \cdot 2} : \frac{3 + 3}{2}

x = \frac{- ( - 6 ) - 2 3}{2 \cdot 2} : \frac{3 - 3}{2}

The solutions to the quadratic equation are:

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

12 x^{2} + 12 x - 826 = 0

2 u^{2} - 5 u - 7

\frac{2}{2 - 1}

9 e - 7 = 7 e - 11

8 (x + 1) + 1 < 3 (2 x) + 1

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