What are the solutions to the equation 3x^2-32x+69=0 ?

The solutions to the equation 3x^2-32x+69=0 are x= 23/3 ,x=3

Find the zeros of 3x^2-32x+69=0

The zeros of 3x^2-32x+69=0 are x= 23/3 ,x=3

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3 x^{2} - 32 x + 69 = 0

x = \frac{23}{3}, x = 3

Decimal Notation

x = 7.66666 \dots, x = 3

Solution steps

3 x^{2} - 32 x + 69 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 32 ) \pm ( - 32 ) ^{2} - 4 \cdot 3 \cdot 69}{2 \cdot 3}

(- 32)^{2} - 4 \cdot 3 \cdot 69 = 14

x_{1, 2} = \frac{- ( - 32 ) \pm 14}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 32 ) + 14}{2 \cdot 3}, x_{2} = \frac{- ( - 32 ) - 14}{2 \cdot 3}

x = \frac{- ( - 32 ) + 14}{2 \cdot 3} : \frac{23}{3}

x = \frac{- ( - 32 ) - 14}{2 \cdot 3} : 3

The solutions to the quadratic equation are:

x = \frac{23}{3}, x = 3

2 n^{2} - 9 n + 5 = 2 n

x^{2} + 4 x - 21 = 0

2 x^{2} + 12 x + 8

6 w^{2} - 26 w + 5 = w^{2}

5 x^{2} = - 28 x + 12

What are the solutions to the equation 3x^2-32x+69=0 ?
The solutions to the equation 3x^2-32x+69=0 are x= 23/3 ,x=3
Find the zeros of 3x^2-32x+69=0
The zeros of 3x^2-32x+69=0 are x= 23/3 ,x=3