What are the solutions to the equation (x^2)/3-x-9/6 = 3/2 ?

The solutions to the equation (x^2)/3-x-9/6 = 3/2 are x=(3(1+sqrt(5)))/2 ,x=(3(1-sqrt(5)))/2

Find the zeros of (x^2)/3-x-9/6 = 3/2

The zeros of (x^2)/3-x-9/6 = 3/2 are x=(3(1+sqrt(5)))/2 ,x=(3(1-sqrt(5)))/2

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\frac{x ^{2}}{3} - x - \frac{9}{6} = \frac{3}{2}

x = \frac{3 ( 1 + 5 )}{2}, x = \frac{3 ( 1 - 5 )}{2}

Decimal Notation

x = 4.85410 \dots, x = - 1.85410 \dots

Solution steps

\frac{x ^{2}}{3} - x - \frac{9}{6} = \frac{3}{2}

Find Least Common Multiplier of

3, 6, 2 : 6

Multiply by LCM=

6

\frac{x ^{2}}{3} \cdot 6 - x \cdot 6 - \frac{9}{6} \cdot 6 = \frac{3}{2} \cdot 6

Simplify

2 x^{2} - 6 x - 9 = 9

Move

9

to the left side

2 x^{2} - 6 x - 18 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 2 ( - 18 )}{2 \cdot 2}

(- 6)^{2} - 4 \cdot 2 (- 18) = 65

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

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 6 5}{2 \cdot 2}, x_{2} = \frac{- ( - 6 ) - 6 5}{2 \cdot 2}

x = \frac{- ( - 6 ) + 6 5}{2 \cdot 2} : \frac{3 ( 1 + 5 )}{2}

x = \frac{- ( - 6 ) - 6 5}{2 \cdot 2} : \frac{3 ( 1 - 5 )}{2}

The solutions to the quadratic equation are:

x = \frac{3 ( 1 + 5 )}{2}, x = \frac{3 ( 1 - 5 )}{2}

x, 3 x^{2} - 6 x y - 4 x y - 8 y^{2} = 0

x, (x - 1)^{2} + (y + 2)^{4} = 0

y, y^{2} (1 + p^{2}) = r^{2}

7 5^{2} = (15 t)^{2} + [12 (t - 2)]^{2}

\frac{3 x ^{2} - x}{3} = 0

What are the solutions to the equation (x^2)/3-x-9/6 = 3/2 ?
The solutions to the equation (x^2)/3-x-9/6 = 3/2 are x=(3(1+sqrt(5)))/2 ,x=(3(1-sqrt(5)))/2
Find the zeros of (x^2)/3-x-9/6 = 3/2
The zeros of (x^2)/3-x-9/6 = 3/2 are x=(3(1+sqrt(5)))/2 ,x=(3(1-sqrt(5)))/2