What are the solutions to the equation (x+3)(x-3)=x(4x+5) ?

The solutions to the equation (x+3)(x-3)=x(4x+5) are x=-5/6-i(sqrt(83))/6 ,x=-5/6+i(sqrt(83))/6

Find the zeros of (x+3)(x-3)=x(4x+5)

The zeros of (x+3)(x-3)=x(4x+5) are x=-5/6-i(sqrt(83))/6 ,x=-5/6+i(sqrt(83))/6

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(x + 3) (x - 3) = x (4 x + 5)

x = - \frac{5}{6} - i \frac{83}{6}, x = - \frac{5}{6} + i \frac{83}{6}

Solution steps

(x + 3) (x - 3) = x (4 x + 5)

Expand

(x + 3) (x - 3) : x^{2} - 9

Expand

x (4 x + 5) : 4 x^{2} + 5 x

x^{2} - 9 = 4 x^{2} + 5 x

Move

5 x

to the left side

x^{2} - 9 - 5 x = 4 x^{2}

Move

4 x^{2}

to the left side

- 3 x^{2} - 5 x - 9 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 ( - 3 ) ( - 9 )}{2 ( - 3 )}

Simplify

(- 5)^{2} - 4 (- 3) (- 9) : 83 i

x_{1, 2} = \frac{- ( - 5 ) \pm 83 i}{2 ( - 3 )}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 83 i}{2 ( - 3 )}, x_{2} = \frac{- ( - 5 ) - 83 i}{2 ( - 3 )}

x = \frac{- ( - 5 ) + 83 i}{2 ( - 3 )} : - \frac{5}{6} - i \frac{83}{6}

x = \frac{- ( - 5 ) - 83 i}{2 ( - 3 )} : - \frac{5}{6} + i \frac{83}{6}

The solutions to the quadratic equation are:

x = - \frac{5}{6} - i \frac{83}{6}, x = - \frac{5}{6} + i \frac{83}{6}

y, y^{2} = 5 - X

3 (x^{2} + 1) = x (x - 3)

x, 2 y x^{2} - 4 x - y + 4 = 0

x^{2} - 24 + 5 x = 0

8 - 3 x = 2 x^{2} - 3 x - 8

What are the solutions to the equation (x+3)(x-3)=x(4x+5) ?
The solutions to the equation (x+3)(x-3)=x(4x+5) are x=-5/6-i(sqrt(83))/6 ,x=-5/6+i(sqrt(83))/6
Find the zeros of (x+3)(x-3)=x(4x+5)
The zeros of (x+3)(x-3)=x(4x+5) are x=-5/6-i(sqrt(83))/6 ,x=-5/6+i(sqrt(83))/6