What are the solutions to the equation 12b^2-83b=27 ?

The solutions to the equation 12b^2-83b=27 are b=(83+sqrt(8185))/(24),b=(83-sqrt(8185))/(24)

Find the zeros of 12b^2-83b=27

The zeros of 12b^2-83b=27 are b=(83+sqrt(8185))/(24),b=(83-sqrt(8185))/(24)

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12 b^{2} - 83 b = 27

b = \frac{83 + 8185}{24}, b = \frac{83 - 8185}{24}

Decimal Notation

b = 7.22795 \dots, b = - 0.31129 \dots

Solution steps

12 b^{2} - 83 b = 27

Move

27

to the left side

12 b^{2} - 83 b - 27 = 0

Solve with the quadratic formula

b_{1, 2} = \frac{- ( - 83 ) \pm ( - 83 ) ^{2} - 4 \cdot 12 ( - 27 )}{2 \cdot 12}

(- 83)^{2} - 4 \cdot 12 (- 27) = 8185

b_{1, 2} = \frac{- ( - 83 ) \pm 8185}{2 \cdot 12}

Separate the solutions

b_{1} = \frac{- ( - 83 ) + 8185}{2 \cdot 12}, b_{2} = \frac{- ( - 83 ) - 8185}{2 \cdot 12}

b = \frac{- ( - 83 ) + 8185}{2 \cdot 12} : \frac{83 + 8185}{24}

b = \frac{- ( - 83 ) - 8185}{2 \cdot 12} : \frac{83 - 8185}{24}

The solutions to the quadratic equation are:

b = \frac{83 + 8185}{24}, b = \frac{83 - 8185}{24}

7 w = \frac{14}{9}

\frac{16}{3}

\frac{12 !}{9 !}

10 = - 2 + x

x^{2} + 6 x - 6 = 0

What are the solutions to the equation 12b^2-83b=27 ?
The solutions to the equation 12b^2-83b=27 are b=(83+sqrt(8185))/(24),b=(83-sqrt(8185))/(24)
Find the zeros of 12b^2-83b=27
The zeros of 12b^2-83b=27 are b=(83+sqrt(8185))/(24),b=(83-sqrt(8185))/(24)