What are the solutions to the equation 3x^2-24x+2=5x^2+1 ?

The solutions to the equation 3x^2-24x+2=5x^2+1 are x=-(12+sqrt(146))/2 ,x=(sqrt(146)-12)/2

Find the zeros of 3x^2-24x+2=5x^2+1

The zeros of 3x^2-24x+2=5x^2+1 are x=-(12+sqrt(146))/2 ,x=(sqrt(146)-12)/2

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3 x^{2} - 24 x + 2 = 5 x^{2} + 1

x = - \frac{12 + 146}{2}, x = \frac{146 - 12}{2}

Decimal Notation

x = - 12.04152 \dots, x = 0.04152 \dots

Solution steps

3 x^{2} - 24 x + 2 = 5 x^{2} + 1

Move

1

to the left side

3 x^{2} - 24 x + 1 = 5 x^{2}

Move

5 x^{2}

to the left side

- 2 x^{2} - 24 x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 ( - 2 ) \cdot 1}{2 ( - 2 )}

(- 24)^{2} - 4 (- 2) \cdot 1 = 2146

x_{1, 2} = \frac{- ( - 24 ) \pm 2 146}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 2 146}{2 ( - 2 )}, x_{2} = \frac{- ( - 24 ) - 2 146}{2 ( - 2 )}

x = \frac{- ( - 24 ) + 2 146}{2 ( - 2 )} : - \frac{12 + 146}{2}

x = \frac{- ( - 24 ) - 2 146}{2 ( - 2 )} : \frac{146 - 12}{2}

The solutions to the quadratic equation are:

x = - \frac{12 + 146}{2}, x = \frac{146 - 12}{2}

2 x^{2} - 8 x + 3

x^{2} + 3 = 28

14 - 6 x^{2} = 0

5 - 3 x^{2} = 0

- 3 x^{2} - 2 x + 1 = 0

What are the solutions to the equation 3x^2-24x+2=5x^2+1 ?
The solutions to the equation 3x^2-24x+2=5x^2+1 are x=-(12+sqrt(146))/2 ,x=(sqrt(146)-12)/2
Find the zeros of 3x^2-24x+2=5x^2+1
The zeros of 3x^2-24x+2=5x^2+1 are x=-(12+sqrt(146))/2 ,x=(sqrt(146)-12)/2