What are the solutions to the equation 24x^2-3x-11=0 ?

The solutions to the equation 24x^2-3x-11=0 are x=(3+sqrt(1065))/(48),x=(3-sqrt(1065))/(48)

Find the zeros of 24x^2-3x-11=0

The zeros of 24x^2-3x-11=0 are x=(3+sqrt(1065))/(48),x=(3-sqrt(1065))/(48)

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24 x^{2} - 3 x - 11 = 0

x = \frac{3 + 1065}{48}, x = \frac{3 - 1065}{48}

Decimal Notation

x = 0.74238 \dots, x = - 0.61738 \dots

Solution steps

24 x^{2} - 3 x - 11 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 24 ( - 11 )}{2 \cdot 24}

(- 3)^{2} - 4 \cdot 24 (- 11) = 1065

x_{1, 2} = \frac{- ( - 3 ) \pm 1065}{2 \cdot 24}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 1065}{2 \cdot 24}, x_{2} = \frac{- ( - 3 ) - 1065}{2 \cdot 24}

x = \frac{- ( - 3 ) + 1065}{2 \cdot 24} : \frac{3 + 1065}{48}

x = \frac{- ( - 3 ) - 1065}{2 \cdot 24} : \frac{3 - 1065}{48}

The solutions to the quadratic equation are:

x = \frac{3 + 1065}{48}, x = \frac{3 - 1065}{48}

12 x^{2} - 168 x + 432 = 0

x, z = y x^{2} z^{2} - x y^{4} + x y

y^{2} = (4430523)^{2} + (3166128)^{2}

15 x^{2} - 23 x - 10 = 0

x, 4 x^{2} + y^{2} + z^{2} = 1

What are the solutions to the equation 24x^2-3x-11=0 ?
The solutions to the equation 24x^2-3x-11=0 are x=(3+sqrt(1065))/(48),x=(3-sqrt(1065))/(48)
Find the zeros of 24x^2-3x-11=0
The zeros of 24x^2-3x-11=0 are x=(3+sqrt(1065))/(48),x=(3-sqrt(1065))/(48)