What are the solutions to the equation 8b^2+16b+19=5b^2 ?

The solutions to the equation 8b^2+16b+19=5b^2 are b=(-8+sqrt(7))/3 ,b=-(8+sqrt(7))/3

Find the zeros of 8b^2+16b+19=5b^2

The zeros of 8b^2+16b+19=5b^2 are b=(-8+sqrt(7))/3 ,b=-(8+sqrt(7))/3

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8 b^{2} + 16 b + 19 = 5 b^{2}

b = \frac{- 8 + 7}{3}, b = - \frac{8 + 7}{3}

Decimal Notation

b = - 1.78474 \dots, b = - 3.54858 \dots

Solution steps

8 b^{2} + 16 b + 19 = 5 b^{2}

Move

5 b^{2}

to the left side

3 b^{2} + 16 b + 19 = 0

Solve with the quadratic formula

b_{1, 2} = \frac{- 16 \pm 1 6 ^{2} - 4 \cdot 3 \cdot 19}{2 \cdot 3}

1 6^{2} - 4 \cdot 3 \cdot 19 = 27

b_{1, 2} = \frac{- 16 \pm 2 7}{2 \cdot 3}

Separate the solutions

b_{1} = \frac{- 16 + 2 7}{2 \cdot 3}, b_{2} = \frac{- 16 - 2 7}{2 \cdot 3}

b = \frac{- 16 + 2 7}{2 \cdot 3} : \frac{- 8 + 7}{3}

b = \frac{- 16 - 2 7}{2 \cdot 3} : - \frac{8 + 7}{3}

The solutions to the quadratic equation are:

b = \frac{- 8 + 7}{3}, b = - \frac{8 + 7}{3}

(x + 1)^{2} = - 25

x^{2} = 2 - x^{2}

x, x^{2} + x y - y^{2} = - 1

4 x^{2} - 3 = 25

- 7 (x - 2)^{2} - 14 = 0

What are the solutions to the equation 8b^2+16b+19=5b^2 ?
The solutions to the equation 8b^2+16b+19=5b^2 are b=(-8+sqrt(7))/3 ,b=-(8+sqrt(7))/3
Find the zeros of 8b^2+16b+19=5b^2
The zeros of 8b^2+16b+19=5b^2 are b=(-8+sqrt(7))/3 ,b=-(8+sqrt(7))/3