What are the solutions to the equation 3sqrt(5)*(x^2+4)+sqrt(13)(x^2+36)=8(3+x) ?

The solutions to the equation 3sqrt(5)*(x^2+4)+sqrt(13)(x^2+36)=8(3+x) are

Find the zeros of 3sqrt(5)*(x^2+4)+sqrt(13)(x^2+36)=8(3+x)

The zeros of 3sqrt(5)*(x^2+4)+sqrt(13)(x^2+36)=8(3+x) are

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35 \cdot (x^{2} + 4) + 13 (x^{2} + 36) = 8 (3 + x)

x = \frac{- 13 + 3 5}{8} + i \frac{- 2054 - 234 5 + 390 65 - 78 13 + 3 790 + 150 65 - 30 13 - 90 5}{16}, x = \frac{- 13 + 3 5}{8} + i \frac{2054 - 234 5 + 390 65 - 78 13 - 3 790 + 150 65 - 30 13 - 90 5}{16}

Solution steps

35 (x^{2} + 4) + 13 (x^{2} + 36) = 8 (3 + x)

Expand

35 (x^{2} + 4) + 13 (x^{2} + 36) : 35 x^{2} + 125 + 13 x^{2} + 3613

Expand

8 (3 + x) : 24 + 8 x

35 x^{2} + 125 + 13 x^{2} + 3613 = 24 + 8 x

Move

8 x

to the left side

35 x^{2} + 125 + 13 x^{2} + 3613 - 8 x = 24

Move

24

to the left side

35 x^{2} + 125 + 13 x^{2} + 3613 - 8 x - 24 = 0

Write in the standard form

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

(35 + 13) x^{2} - 8 x + 125 + 3613 - 24 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 ( 3 5 + 13 ) ( 12 5 + 36 13 - 24 )}{2 ( 3 5 + 13 )}

Simplify

(- 8)^{2} - 4 (35 + 13) (125 + 3613 - 24) : i 2528 + 48065 - 2885 - 9613

x_{1, 2} = \frac{- ( - 8 ) \pm i 2528 + 480 65 - 288 5 - 96 13}{2 ( 3 5 + 13 )}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + i 2528 + 480 65 - 288 5 - 96 13}{2 ( 3 5 + 13 )}, x_{2} = \frac{- ( - 8 ) - i 2528 + 480 65 - 288 5 - 96 13}{2 ( 3 5 + 13 )}

x = \frac{- ( - 8 ) + i 2528 + 480 65 - 288 5 - 96 13}{2 ( 3 5 + 13 )} : \frac{- 13 + 3 5}{8} + i \frac{- 2054 - 234 5 + 390 65 - 78 13 + 3 790 + 150 65 - 30 13 - 90 5}{16}

x = \frac{- ( - 8 ) - i 2528 + 480 65 - 288 5 - 96 13}{2 ( 3 5 + 13 )} : \frac{- 13 + 3 5}{8} + i \frac{2054 - 234 5 + 390 65 - 78 13 - 3 790 + 150 65 - 30 13 - 90 5}{16}

The solutions to the quadratic equation are:

x = \frac{- 13 + 3 5}{8} + i \frac{- 2054 - 234 5 + 390 65 - 78 13 + 3 790 + 150 65 - 30 13 - 90 5}{16}, x = \frac{- 13 + 3 5}{8} + i \frac{2054 - 234 5 + 390 65 - 78 13 - 3 790 + 150 65 - 30 13 - 90 5}{16}

- 5 x = - 25

\frac{10 a}{2}

3 x^{2} + 11 x + 10 = 0

x^{2} - 48 = 2 x

x + \frac{13}{30} = - \frac{7}{30}

What are the solutions to the equation 3sqrt(5)*(x^2+4)+sqrt(13)(x^2+36)=8(3+x) ?
The solutions to the equation 3sqrt(5)*(x^2+4)+sqrt(13)(x^2+36)=8(3+x) are
Find the zeros of 3sqrt(5)*(x^2+4)+sqrt(13)(x^2+36)=8(3+x)
The zeros of 3sqrt(5)*(x^2+4)+sqrt(13)(x^2+36)=8(3+x) are