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

The solutions to the equation (x^2)/6-x/2 =3(x-5) are x=15,x=6

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

The zeros of (x^2)/6-x/2 =3(x-5) are x=15,x=6

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

x = 15, x = 6

Solution steps

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

Find Least Common Multiplier of

6, 2 : 6

Multiply by LCM=

6

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

Simplify

x^{2} - 3 x = 18 (x - 5)

Expand

18 (x - 5) : 18 x - 90

x^{2} - 3 x = 18 x - 90

Move

90

to the left side

x^{2} - 3 x + 90 = 18 x

Move

18 x

to the left side

x^{2} - 21 x + 90 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 21 ) \pm ( - 21 ) ^{2} - 4 \cdot 1 \cdot 90}{2 \cdot 1}

(- 21)^{2} - 4 \cdot 1 \cdot 90 = 9

x_{1, 2} = \frac{- ( - 21 ) \pm 9}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 21 ) + 9}{2 \cdot 1}, x_{2} = \frac{- ( - 21 ) - 9}{2 \cdot 1}

x = \frac{- ( - 21 ) + 9}{2 \cdot 1} : 15

x = \frac{- ( - 21 ) - 9}{2 \cdot 1} : 6

The solutions to the quadratic equation are:

x = 15, x = 6

2 x^{2} - 4 x - 3 = (x - 3) (x + 1) - 2 x^{2}

2 r^{2} - 12 r + 12 = - 3

x^{2} = 16 x - 65

x^{2} - 22 x + 121 = 1

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

What are the solutions to the equation (x^2)/6-x/2 =3(x-5) ?
The solutions to the equation (x^2)/6-x/2 =3(x-5) are x=15,x=6
Find the zeros of (x^2)/6-x/2 =3(x-5)
The zeros of (x^2)/6-x/2 =3(x-5) are x=15,x=6