What are the solutions to the equation 6x^2-46x+312=14x ?

The solutions to the equation 6x^2-46x+312=14x are x=5+3sqrt(3)i,x=5-3sqrt(3)i

Find the zeros of 6x^2-46x+312=14x

The zeros of 6x^2-46x+312=14x are x=5+3sqrt(3)i,x=5-3sqrt(3)i

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6 x^{2} - 46 x + 312 = 14 x

x = 5 + 33 i, x = 5 - 33 i

Solution steps

6 x^{2} - 46 x + 312 = 14 x

Move

14 x

to the left side

6 x^{2} - 60 x + 312 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 60 ) \pm ( - 60 ) ^{2} - 4 \cdot 6 \cdot 312}{2 \cdot 6}

Simplify

(- 60)^{2} - 4 \cdot 6 \cdot 312 : 363 i

x_{1, 2} = \frac{- ( - 60 ) \pm 36 3 i}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 60 ) + 36 3 i}{2 \cdot 6}, x_{2} = \frac{- ( - 60 ) - 36 3 i}{2 \cdot 6}

x = \frac{- ( - 60 ) + 36 3 i}{2 \cdot 6} : 5 + 33 i

x = \frac{- ( - 60 ) - 36 3 i}{2 \cdot 6} : 5 - 33 i

The solutions to the quadratic equation are:

x = 5 + 33 i, x = 5 - 33 i

\frac{n ( n - 3 )}{2} = 2 n

\frac{n ( n - 3 )}{2} = 27

2 x^{2} - 10 = 64

x^{2} - 8 x + 45 = 0

x^{2} + 7 x - 18 = 0

What are the solutions to the equation 6x^2-46x+312=14x ?
The solutions to the equation 6x^2-46x+312=14x are x=5+3sqrt(3)i,x=5-3sqrt(3)i
Find the zeros of 6x^2-46x+312=14x
The zeros of 6x^2-46x+312=14x are x=5+3sqrt(3)i,x=5-3sqrt(3)i