What are the solutions to the equation 3x^2-31x+60=0 ?

The solutions to the equation 3x^2-31x+60=0 are x=(31+sqrt(241))/6 ,x=(31-sqrt(241))/6

Find the zeros of 3x^2-31x+60=0

The zeros of 3x^2-31x+60=0 are x=(31+sqrt(241))/6 ,x=(31-sqrt(241))/6

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3 x^{2} - 31 x + 60 = 0

x = \frac{31 + 241}{6}, x = \frac{31 - 241}{6}

Decimal

x = 7.75402 \dots, x = 2.57930 \dots

Solution steps

3 x^{2} - 31 x + 60 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 31 ) \pm ( - 31 ) ^{2} - 4 \cdot 3 \cdot 60}{2 \cdot 3}

(- 31)^{2} - 4 \cdot 3 \cdot 60 = 241

x_{1, 2} = \frac{- ( - 31 ) \pm 241}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 31 ) + 241}{2 \cdot 3}, x_{2} = \frac{- ( - 31 ) - 241}{2 \cdot 3}

x = \frac{- ( - 31 ) + 241}{2 \cdot 3} : \frac{31 + 241}{6}

x = \frac{- ( - 31 ) - 241}{2 \cdot 3} : \frac{31 - 241}{6}

The solutions to the quadratic equation are:

x = \frac{31 + 241}{6}, x = \frac{31 - 241}{6}

y, 3 x^{2} - 3 + 3 y^{2} = 6 x y

(\frac{x}{3})^{2} = 81

x^{2} - 12 x + 36 = 13

x^{2} - 12 x + 36 = 20

x^{2} = \frac{x}{2}

What are the solutions to the equation 3x^2-31x+60=0 ?
The solutions to the equation 3x^2-31x+60=0 are x=(31+sqrt(241))/6 ,x=(31-sqrt(241))/6
Find the zeros of 3x^2-31x+60=0
The zeros of 3x^2-31x+60=0 are x=(31+sqrt(241))/6 ,x=(31-sqrt(241))/6