What are the solutions to the equation 12x^2-240x+819=0 ?

The solutions to the equation 12x^2-240x+819=0 are x=(20+sqrt(127))/2 ,x=(20-sqrt(127))/2

Find the zeros of 12x^2-240x+819=0

The zeros of 12x^2-240x+819=0 are x=(20+sqrt(127))/2 ,x=(20-sqrt(127))/2

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12 x^{2} - 240 x + 819 = 0

x = \frac{20 + 127}{2}, x = \frac{20 - 127}{2}

Decimal Notation

x = 15.63471 \dots, x = 4.36528 \dots

Solution steps

12 x^{2} - 240 x + 819 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 240 ) \pm ( - 240 ) ^{2} - 4 \cdot 12 \cdot 819}{2 \cdot 12}

(- 240)^{2} - 4 \cdot 12 \cdot 819 = 12127

x_{1, 2} = \frac{- ( - 240 ) \pm 12 127}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 240 ) + 12 127}{2 \cdot 12}, x_{2} = \frac{- ( - 240 ) - 12 127}{2 \cdot 12}

x = \frac{- ( - 240 ) + 12 127}{2 \cdot 12} : \frac{20 + 127}{2}

x = \frac{- ( - 240 ) - 12 127}{2 \cdot 12} : \frac{20 - 127}{2}

The solutions to the quadratic equation are:

x = \frac{20 + 127}{2}, x = \frac{20 - 127}{2}

8 x^{2} - 12 x = 0

6 x^{2} - 18 x - 240 = 0

2 b^{2} + 11 b + 7 = 0

x^{2} + 15 x + 60 = 4

16 (x^{2} - 6) + 5 = - 10

What are the solutions to the equation 12x^2-240x+819=0 ?
The solutions to the equation 12x^2-240x+819=0 are x=(20+sqrt(127))/2 ,x=(20-sqrt(127))/2
Find the zeros of 12x^2-240x+819=0
The zeros of 12x^2-240x+819=0 are x=(20+sqrt(127))/2 ,x=(20-sqrt(127))/2