What are the solutions to the equation 12+2.4x-3x^2=0 ?

The solutions to the equation 12+2.4x-3x^2=0 are x=-(2(sqrt(26)-1))/5 ,x=(2(1+sqrt(26)))/5

Find the zeros of 12+2.4x-3x^2=0

The zeros of 12+2.4x-3x^2=0 are x=-(2(sqrt(26)-1))/5 ,x=(2(1+sqrt(26)))/5

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12 + 2.4 x - 3 x^{2} = 0

x = - \frac{2 ( 26 - 1 )}{5}, x = \frac{2 ( 1 + 26 )}{5}

Decimal Notation

x = - 1.63960 \dots, x = 2.43960 \dots

Solution steps

12 + 2.4 x - 3 x^{2} = 0

Multiply both sides by

10

120 + 24 x - 30 x^{2} = 0

Write in the standard form

a x^{2} + b x + c = 0

- 30 x^{2} + 24 x + 120 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 24 \pm 2 4 ^{2} - 4 ( - 30 ) \cdot 120}{2 ( - 30 )}

2 4^{2} - 4 (- 30) \cdot 120 = 2426

x_{1, 2} = \frac{- 24 \pm 24 26}{2 ( - 30 )}

Separate the solutions

x_{1} = \frac{- 24 + 24 26}{2 ( - 30 )}, x_{2} = \frac{- 24 - 24 26}{2 ( - 30 )}

x = \frac{- 24 + 24 26}{2 ( - 30 )} : - \frac{2 ( 26 - 1 )}{5}

x = \frac{- 24 - 24 26}{2 ( - 30 )} : \frac{2 ( 1 + 26 )}{5}

The solutions to the quadratic equation are:

x = - \frac{2 ( 26 - 1 )}{5}, x = \frac{2 ( 1 + 26 )}{5}

\frac{1}{3} x^{2} + \frac{1}{3} x - \frac{2}{3} = 0

- 3 x^{2} + 12 x + 8 = 0

x^{2} - 4 x + 14 = 13

3 x^{2} - 2 x + 18 = 0

2 x^{2} + 7 x - 13 = - 10

What are the solutions to the equation 12+2.4x-3x^2=0 ?
The solutions to the equation 12+2.4x-3x^2=0 are x=-(2(sqrt(26)-1))/5 ,x=(2(1+sqrt(26)))/5
Find the zeros of 12+2.4x-3x^2=0
The zeros of 12+2.4x-3x^2=0 are x=-(2(sqrt(26)-1))/5 ,x=(2(1+sqrt(26)))/5