What are the solutions to the equation 9r(r-2)=r^2+5 ?

The solutions to the equation 9r(r-2)=r^2+5 are r= 5/2 ,r=-1/4

Find the zeros of 9r(r-2)=r^2+5

The zeros of 9r(r-2)=r^2+5 are r= 5/2 ,r=-1/4

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9 r (r - 2) = r^{2} + 5

r = \frac{5}{2}, r = - \frac{1}{4}

Decimal Notation

r = 2.5, r = - 0.25

Solution steps

9 r (r - 2) = r^{2} + 5

Expand

9 r (r - 2) : 9 r^{2} - 18 r

9 r^{2} - 18 r = r^{2} + 5

Move

5

to the left side

9 r^{2} - 18 r - 5 = r^{2}

Move

r^{2}

to the left side

8 r^{2} - 18 r - 5 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 8 ( - 5 )}{2 \cdot 8}

(- 18)^{2} - 4 \cdot 8 (- 5) = 22

r_{1, 2} = \frac{- ( - 18 ) \pm 22}{2 \cdot 8}

Separate the solutions

r_{1} = \frac{- ( - 18 ) + 22}{2 \cdot 8}, r_{2} = \frac{- ( - 18 ) - 22}{2 \cdot 8}

r = \frac{- ( - 18 ) + 22}{2 \cdot 8} : \frac{5}{2}

r = \frac{- ( - 18 ) - 22}{2 \cdot 8} : - \frac{1}{4}

The solutions to the quadratic equation are:

r = \frac{5}{2}, r = - \frac{1}{4}

x^{2} + 8 x + 3 = 0

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

y, - 3 y^{2} z - 3 y z^{2} = 21

p^{2} + 14 p + 49 = 2

w^{2} + 16 w + 64 = 0

What are the solutions to the equation 9r(r-2)=r^2+5 ?
The solutions to the equation 9r(r-2)=r^2+5 are r= 5/2 ,r=-1/4
Find the zeros of 9r(r-2)=r^2+5
The zeros of 9r(r-2)=r^2+5 are r= 5/2 ,r=-1/4