What are the solutions to the equation (x^2)/3-x= 5/6 ?

The solutions to the equation (x^2)/3-x= 5/6 are x=(3+sqrt(19))/2 ,x=(3-sqrt(19))/2

Find the zeros of (x^2)/3-x= 5/6

The zeros of (x^2)/3-x= 5/6 are x=(3+sqrt(19))/2 ,x=(3-sqrt(19))/2

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\frac{x ^{2}}{3} - x = \frac{5}{6}

x = \frac{3 + 19}{2}, x = \frac{3 - 19}{2}

Decimal Notation

x = 3.67944 \dots, x = - 0.67944 \dots

Solution steps

\frac{x ^{2}}{3} - x = \frac{5}{6}

Find Least Common Multiplier of

3, 6 : 6

Multiply by LCM=

6

\frac{x ^{2}}{3} \cdot 6 - x \cdot 6 = \frac{5}{6} \cdot 6

Simplify

2 x^{2} - 6 x = 5

Move

5

to the left side

2 x^{2} - 6 x - 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 2 ( - 5 )}{2 \cdot 2}

(- 6)^{2} - 4 \cdot 2 (- 5) = 219

x_{1, 2} = \frac{- ( - 6 ) \pm 2 19}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 19}{2 \cdot 2}, x_{2} = \frac{- ( - 6 ) - 2 19}{2 \cdot 2}

x = \frac{- ( - 6 ) + 2 19}{2 \cdot 2} : \frac{3 + 19}{2}

x = \frac{- ( - 6 ) - 2 19}{2 \cdot 2} : \frac{3 - 19}{2}

The solutions to the quadratic equation are:

x = \frac{3 + 19}{2}, x = \frac{3 - 19}{2}

x^{2} - 19 x + 32 = 0

2 x^{2} + 8 x - 9 = 0

x^{2} - 14 x + 16 = 0

11 n^{2} + 3 = - 12 n

x, f = - x^{2} + (k + 4) x - 5

What are the solutions to the equation (x^2)/3-x= 5/6 ?
The solutions to the equation (x^2)/3-x= 5/6 are x=(3+sqrt(19))/2 ,x=(3-sqrt(19))/2
Find the zeros of (x^2)/3-x= 5/6
The zeros of (x^2)/3-x= 5/6 are x=(3+sqrt(19))/2 ,x=(3-sqrt(19))/2