What are the solutions to the equation 6-2x^2=6x ?

The solutions to the equation 6-2x^2=6x are x=-(3+sqrt(21))/2 ,x=(sqrt(21)-3)/2

Find the zeros of 6-2x^2=6x

The zeros of 6-2x^2=6x are x=-(3+sqrt(21))/2 ,x=(sqrt(21)-3)/2

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6 - 2 x^{2} = 6 x

x = - \frac{3 + 21}{2}, x = \frac{21 - 3}{2}

Solution steps

6 - 2 x^{2} = 6 x

Move

6 x

to the left side

6 - 2 x^{2} - 6 x = 0

Write in the standard form

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

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

Solve with the quadratic formula

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

(- 6)^{2} - 4 (- 2) \cdot 6 = 221

x_{1, 2} = \frac{- ( - 6 ) \pm 2 21}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 2 21}{2 ( - 2 )}, x_{2} = \frac{- ( - 6 ) - 2 21}{2 ( - 2 )}

x = \frac{- ( - 6 ) + 2 21}{2 ( - 2 )} : - \frac{3 + 21}{2}

x = \frac{- ( - 6 ) - 2 21}{2 ( - 2 )} : \frac{21 - 3}{2}

The solutions to the quadratic equation are:

x = - \frac{3 + 21}{2}, x = \frac{21 - 3}{2}

x^{2} + 40 = - 14 x

x^{2} + 2 = 4 x

- (x - 6)^{2} + 6 = - 11

9 x^{2} - 6 x + 1 = 0

- 4 x^{2} + 7 x - 1 = 0

What are the solutions to the equation 6-2x^2=6x ?
The solutions to the equation 6-2x^2=6x are x=-(3+sqrt(21))/2 ,x=(sqrt(21)-3)/2
Find the zeros of 6-2x^2=6x
The zeros of 6-2x^2=6x are x=-(3+sqrt(21))/2 ,x=(sqrt(21)-3)/2