What are the solutions to the equation 3x^2-20x+31=0 ?

The solutions to the equation 3x^2-20x+31=0 are x=(10+sqrt(7))/3 ,x=(10-sqrt(7))/3

Find the zeros of 3x^2-20x+31=0

The zeros of 3x^2-20x+31=0 are x=(10+sqrt(7))/3 ,x=(10-sqrt(7))/3

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3 x^{2} - 20 x + 31 = 0

x = \frac{10 + 7}{3}, x = \frac{10 - 7}{3}

Decimal Notation

x = 4.21525 \dots, x = 2.45141 \dots

Solution steps

3 x^{2} - 20 x + 31 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 20 ) \pm ( - 20 ) ^{2} - 4 \cdot 3 \cdot 31}{2 \cdot 3}

(- 20)^{2} - 4 \cdot 3 \cdot 31 = 27

x_{1, 2} = \frac{- ( - 20 ) \pm 2 7}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 20 ) + 2 7}{2 \cdot 3}, x_{2} = \frac{- ( - 20 ) - 2 7}{2 \cdot 3}

x = \frac{- ( - 20 ) + 2 7}{2 \cdot 3} : \frac{10 + 7}{3}

x = \frac{- ( - 20 ) - 2 7}{2 \cdot 3} : \frac{10 - 7}{3}

The solutions to the quadratic equation are:

x = \frac{10 + 7}{3}, x = \frac{10 - 7}{3}

(x - 1)^{2} + 3 = 0

x, x^{2} - m x + m - 1 = 0

60 + 4 t - 4.9 t^{2} = 0

X^{2} - 5 X - 4 = 0

ρ^{2} - 3 ρ + 2 = 0

What are the solutions to the equation 3x^2-20x+31=0 ?
The solutions to the equation 3x^2-20x+31=0 are x=(10+sqrt(7))/3 ,x=(10-sqrt(7))/3
Find the zeros of 3x^2-20x+31=0
The zeros of 3x^2-20x+31=0 are x=(10+sqrt(7))/3 ,x=(10-sqrt(7))/3