What are the solutions to the equation 27x^2+bx+3=0 ?

The solutions to the equation 27x^2+bx+3=0 are x=(-b+sqrt(b^2-324))/(54),x=(-b-sqrt(b^2-324))/(54)

Find the zeros of 27x^2+bx+3=0

The zeros of 27x^2+bx+3=0 are x=(-b+sqrt(b^2-324))/(54),x=(-b-sqrt(b^2-324))/(54)

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27 x^{2} + b x + 3 = 0

x = \frac{- b + b ^{2} - 324}{54}, x = \frac{- b - b ^{2} - 324}{54}

Solution steps

27 x^{2} + b x + 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- b \pm b ^{2} - 4 \cdot 27 \cdot 3}{2 \cdot 27}

Simplify

b^{2} - 4 \cdot 27 \cdot 3 : b^{2} - 324

x_{1, 2} = \frac{- b \pm b ^{2} - 324}{2 \cdot 27}

Separate the solutions

x_{1} = \frac{- b + b ^{2} - 324}{2 \cdot 27}, x_{2} = \frac{- b - b ^{2} - 324}{2 \cdot 27}

x = \frac{- b + b ^{2} - 324}{2 \cdot 27} : \frac{- b + b ^{2} - 324}{54}

x = \frac{- b - b ^{2} - 324}{2 \cdot 27} : \frac{- b - b ^{2} - 324}{54}

The solutions to the quadratic equation are:

x = \frac{- b + b ^{2} - 324}{54}, x = \frac{- b - b ^{2} - 324}{54}

4 x^{2} + 28 x = - 53

6 x^{2} + 2 x = 3

48 a^{2} - 279 a = - 210 + 3 a

24 x^{2} + 2 x = 15

(x + 5) (x - 3) = 0

What are the solutions to the equation 27x^2+bx+3=0 ?
The solutions to the equation 27x^2+bx+3=0 are x=(-b+sqrt(b^2-324))/(54),x=(-b-sqrt(b^2-324))/(54)
Find the zeros of 27x^2+bx+3=0
The zeros of 27x^2+bx+3=0 are x=(-b+sqrt(b^2-324))/(54),x=(-b-sqrt(b^2-324))/(54)