What are the solutions to the equation 9x^2+83=54x ?

The solutions to the equation 9x^2+83=54x are x=3+i(sqrt(2))/3 ,x=3-i(sqrt(2))/3

Find the zeros of 9x^2+83=54x

The zeros of 9x^2+83=54x are x=3+i(sqrt(2))/3 ,x=3-i(sqrt(2))/3

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9 x^{2} + 83 = 54 x

x = 3 + i \frac{2}{3}, x = 3 - i \frac{2}{3}

Solution steps

9 x^{2} + 83 = 54 x

Move

54 x

to the left side

9 x^{2} + 83 - 54 x = 0

Write in the standard form

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

9 x^{2} - 54 x + 83 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 54 ) \pm ( - 54 ) ^{2} - 4 \cdot 9 \cdot 83}{2 \cdot 9}

Simplify

(- 54)^{2} - 4 \cdot 9 \cdot 83 : 62 i

x_{1, 2} = \frac{- ( - 54 ) \pm 6 2 i}{2 \cdot 9}

Separate the solutions

x_{1} = \frac{- ( - 54 ) + 6 2 i}{2 \cdot 9}, x_{2} = \frac{- ( - 54 ) - 6 2 i}{2 \cdot 9}

x = \frac{- ( - 54 ) + 6 2 i}{2 \cdot 9} : 3 + i \frac{2}{3}

x = \frac{- ( - 54 ) - 6 2 i}{2 \cdot 9} : 3 - i \frac{2}{3}

The solutions to the quadratic equation are:

x = 3 + i \frac{2}{3}, x = 3 - i \frac{2}{3}

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What are the solutions to the equation 9x^2+83=54x ?
The solutions to the equation 9x^2+83=54x are x=3+i(sqrt(2))/3 ,x=3-i(sqrt(2))/3
Find the zeros of 9x^2+83=54x
The zeros of 9x^2+83=54x are x=3+i(sqrt(2))/3 ,x=3-i(sqrt(2))/3