What are the solutions to the equation 3a^2-2a-32=-9 ?

The solutions to the equation 3a^2-2a-32=-9 are a=(1+sqrt(70))/3 ,a=(1-sqrt(70))/3

Find the zeros of 3a^2-2a-32=-9

The zeros of 3a^2-2a-32=-9 are a=(1+sqrt(70))/3 ,a=(1-sqrt(70))/3

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3 a^{2} - 2 a - 32 = - 9

a = \frac{1 + 70}{3}, a = \frac{1 - 70}{3}

Decimal Notation

a = 3.12220 \dots, a = - 2.45553 \dots

Solution steps

3 a^{2} - 2 a - 32 = - 9

Move

9

to the left side

3 a^{2} - 2 a - 23 = 0

Solve with the quadratic formula

a_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 3 ( - 23 )}{2 \cdot 3}

(- 2)^{2} - 4 \cdot 3 (- 23) = 270

a_{1, 2} = \frac{- ( - 2 ) \pm 2 70}{2 \cdot 3}

Separate the solutions

a_{1} = \frac{- ( - 2 ) + 2 70}{2 \cdot 3}, a_{2} = \frac{- ( - 2 ) - 2 70}{2 \cdot 3}

a = \frac{- ( - 2 ) + 2 70}{2 \cdot 3} : \frac{1 + 70}{3}

a = \frac{- ( - 2 ) - 2 70}{2 \cdot 3} : \frac{1 - 70}{3}

The solutions to the quadratic equation are:

a = \frac{1 + 70}{3}, a = \frac{1 - 70}{3}

x^{2} + 23 = - 10 x

3 x^{2} + 64 = 33 x - 8

r^{2} + 14 r + 49 = 0

8 x^{2} + 18 x = 5

- 4 x^{2} - 5 x - 1 = 0

What are the solutions to the equation 3a^2-2a-32=-9 ?
The solutions to the equation 3a^2-2a-32=-9 are a=(1+sqrt(70))/3 ,a=(1-sqrt(70))/3
Find the zeros of 3a^2-2a-32=-9
The zeros of 3a^2-2a-32=-9 are a=(1+sqrt(70))/3 ,a=(1-sqrt(70))/3