What are the solutions to the equation ((x^2))/9-x/2 = 1/3+x/9 ?

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

Find the zeros of ((x^2))/9-x/2 = 1/3+x/9

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

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\frac{( x ^{2} )}{9} - \frac{x}{2} = \frac{1}{3} + \frac{x}{9}

x = 6, x = - \frac{1}{2}

Decimal Notation

x = 6, x = - 0.5

Solution steps

\frac{( x ^{2} )}{9} - \frac{x}{2} = \frac{1}{3} + \frac{x}{9}

Find Least Common Multiplier of

9, 2, 3 : 18

Multiply by LCM=

18

\frac{x ^{2}}{9} \cdot 18 - \frac{x}{2} \cdot 18 = \frac{1}{3} \cdot 18 + \frac{x}{9} \cdot 18

Simplify

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

Move

2 x

to the left side

2 x^{2} - 11 x = 6

Move

6

to the left side

2 x^{2} - 11 x - 6 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 11 ) \pm ( - 11 ) ^{2} - 4 \cdot 2 ( - 6 )}{2 \cdot 2}

(- 11)^{2} - 4 \cdot 2 (- 6) = 13

x_{1, 2} = \frac{- ( - 11 ) \pm 13}{2 \cdot 2}

Separate the solutions

x_{1} = \frac{- ( - 11 ) + 13}{2 \cdot 2}, x_{2} = \frac{- ( - 11 ) - 13}{2 \cdot 2}

x = \frac{- ( - 11 ) + 13}{2 \cdot 2} : 6

x = \frac{- ( - 11 ) - 13}{2 \cdot 2} : - \frac{1}{2}

The solutions to the quadratic equation are:

x = 6, x = - \frac{1}{2}

x, x^{2} + y^{2} = b^{2}

x, \frac{x ^{2}}{6 ^{2}} + 8 \frac{y ^{2}}{9 ^{2}} = 0

x = x^{2} - 4 x - 12

(2) 2 m^{2} - 5 m = 0, \frac{5}{2}, m = 2

- 1.25 x^{2} + 35 x - 175 = 50

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