What are the solutions to the equation 9r^2+21r+9=r^2 ?

The solutions to the equation 9r^2+21r+9=r^2 are r=(-21+3sqrt(17))/(16),r=(-21-3sqrt(17))/(16)

Find the zeros of 9r^2+21r+9=r^2

The zeros of 9r^2+21r+9=r^2 are r=(-21+3sqrt(17))/(16),r=(-21-3sqrt(17))/(16)

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9 r^{2} + 21 r + 9 = r^{2}

r = \frac{- 21 + 3 17}{16}, r = \frac{- 21 - 3 17}{16}

Decimal Notation

r = - 0.53941 \dots, r = - 2.08558 \dots

Solution steps

9 r^{2} + 21 r + 9 = r^{2}

Move

r^{2}

to the left side

8 r^{2} + 21 r + 9 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- 21 \pm 2 1 ^{2} - 4 \cdot 8 \cdot 9}{2 \cdot 8}

2 1^{2} - 4 \cdot 8 \cdot 9 = 317

r_{1, 2} = \frac{- 21 \pm 3 17}{2 \cdot 8}

Separate the solutions

r_{1} = \frac{- 21 + 3 17}{2 \cdot 8}, r_{2} = \frac{- 21 - 3 17}{2 \cdot 8}

r = \frac{- 21 + 3 17}{2 \cdot 8} : \frac{- 21 + 3 17}{16}

r = \frac{- 21 - 3 17}{2 \cdot 8} : \frac{- 21 - 3 17}{16}

The solutions to the quadratic equation are:

r = \frac{- 21 + 3 17}{16}, r = \frac{- 21 - 3 17}{16}

(2 x^{2} + 3) = 8 x + 3

6 x^{2} - 4 x - 5 = 0

x (3)^{2} + 3 x^{2} - 3 + 3^{2} = 0

2 r^{2} + 9 r + 4 = 0

5 x^{2} - 31 x + 30 = 0

What are the solutions to the equation 9r^2+21r+9=r^2 ?
The solutions to the equation 9r^2+21r+9=r^2 are r=(-21+3sqrt(17))/(16),r=(-21-3sqrt(17))/(16)
Find the zeros of 9r^2+21r+9=r^2
The zeros of 9r^2+21r+9=r^2 are r=(-21+3sqrt(17))/(16),r=(-21-3sqrt(17))/(16)