What are the solutions to the equation 54=(x(x-3))/2 ?

The solutions to the equation 54=(x(x-3))/2 are x=12,x=-9

Find the zeros of 54=(x(x-3))/2

The zeros of 54=(x(x-3))/2 are x=12,x=-9

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54 = \frac{x ( x - 3 )}{2}

x = 12, x = - 9

Solution steps

54 = \frac{x ( x - 3 )}{2}

Multiply both sides by

2

108 = x (x - 3)

Expand

x (x - 3) : x^{2} - 3 x

108 = x^{2} - 3 x

Switch sides

x^{2} - 3 x = 108

Move

108

to the left side

x^{2} - 3 x - 108 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot ( - 108 )}{2 \cdot 1}

(- 3)^{2} - 4 \cdot 1 \cdot (- 108) = 21

x_{1, 2} = \frac{- ( - 3 ) \pm 21}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 21}{2 \cdot 1}, x_{2} = \frac{- ( - 3 ) - 21}{2 \cdot 1}

x = \frac{- ( - 3 ) + 21}{2 \cdot 1} : 12

x = \frac{- ( - 3 ) - 21}{2 \cdot 1} : - 9

The solutions to the quadratic equation are:

x = 12, x = - 9

\frac{12 x ^{6} y ^{- 4} z ^{2}}{3 x ^{2} y ^{- 6} z ^{3}}

\frac{1}{16} x^{4} + 4 x^{2} + 64

\frac{1}{2} x^{2} + 3 x - 3.5

i

x (x - 2) = 0

What are the solutions to the equation 54=(x(x-3))/2 ?
The solutions to the equation 54=(x(x-3))/2 are x=12,x=-9
Find the zeros of 54=(x(x-3))/2
The zeros of 54=(x(x-3))/2 are x=12,x=-9