What are the solutions to the equation 3/4 (x^2-27)=-(9x)/2 ?

The solutions to the equation 3/4 (x^2-27)=-(9x)/2 are x=3,x=-9

Find the zeros of 3/4 (x^2-27)=-(9x)/2

The zeros of 3/4 (x^2-27)=-(9x)/2 are x=3,x=-9

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\frac{3}{4} (x^{2} - 27) = - \frac{9 x}{2}

x = 3, x = - 9

Solution steps

\frac{3}{4} (x^{2} - 27) = - \frac{9 x}{2}

Find Least Common Multiplier of

4, 2 : 4

Multiply by LCM=

4

\frac{3}{4} (x^{2} - 27) \cdot 4 = - \frac{9 x}{2} \cdot 4

Simplify

3 (x^{2} - 27) = - 18 x

Expand

3 (x^{2} - 27) : 3 x^{2} - 81

3 x^{2} - 81 = - 18 x

Move

18 x

to the left side

3 x^{2} - 81 + 18 x = 0

Write in the standard form

a x^{2} + b x + c = 0

3 x^{2} + 18 x - 81 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 18 \pm 1 8 ^{2} - 4 \cdot 3 ( - 81 )}{2 \cdot 3}

1 8^{2} - 4 \cdot 3 (- 81) = 36

x_{1, 2} = \frac{- 18 \pm 36}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- 18 + 36}{2 \cdot 3}, x_{2} = \frac{- 18 - 36}{2 \cdot 3}

x = \frac{- 18 + 36}{2 \cdot 3} : 3

x = \frac{- 18 - 36}{2 \cdot 3} : - 9

The solutions to the quadratic equation are:

x = 3, x = - 9

x, x^{2} + (s + t) x + s t = 0

x^{2} - 6 x + 5 = 12

x^{2} - 6 x + 5 = - 8

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

5 0^{2} = x^{2} + x^{2}

What are the solutions to the equation 3/4 (x^2-27)=-(9x)/2 ?
The solutions to the equation 3/4 (x^2-27)=-(9x)/2 are x=3,x=-9
Find the zeros of 3/4 (x^2-27)=-(9x)/2
The zeros of 3/4 (x^2-27)=-(9x)/2 are x=3,x=-9