What are the solutions to the equation 4x^2-16x-3=0 ?

The solutions to the equation 4x^2-16x-3=0 are x=(4+sqrt(19))/2 ,x=(4-sqrt(19))/2

Find the zeros of 4x^2-16x-3=0

The zeros of 4x^2-16x-3=0 are x=(4+sqrt(19))/2 ,x=(4-sqrt(19))/2

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4 x^{2} - 16 x - 3 = 0

x = \frac{4 + 19}{2}, x = \frac{4 - 19}{2}

Decimal Notation

x = 4.17944 \dots, x = - 0.17944 \dots

Solution steps

4 x^{2} - 16 x - 3 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 16 ) \pm ( - 16 ) ^{2} - 4 \cdot 4 ( - 3 )}{2 \cdot 4}

(- 16)^{2} - 4 \cdot 4 (- 3) = 419

x_{1, 2} = \frac{- ( - 16 ) \pm 4 19}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 16 ) + 4 19}{2 \cdot 4}, x_{2} = \frac{- ( - 16 ) - 4 19}{2 \cdot 4}

x = \frac{- ( - 16 ) + 4 19}{2 \cdot 4} : \frac{4 + 19}{2}

x = \frac{- ( - 16 ) - 4 19}{2 \cdot 4} : \frac{4 - 19}{2}

The solutions to the quadratic equation are:

x = \frac{4 + 19}{2}, x = \frac{4 - 19}{2}

t, s = 80 t - 16 t^{2}

2 x^{2} - 8 x - 18 = 0

18 x^{2} - 45 x = 0

3 n^{2} - 8 n - 26 = 9

x, x^{2} + y^{2} = a^{2}

What are the solutions to the equation 4x^2-16x-3=0 ?
The solutions to the equation 4x^2-16x-3=0 are x=(4+sqrt(19))/2 ,x=(4-sqrt(19))/2
Find the zeros of 4x^2-16x-3=0
The zeros of 4x^2-16x-3=0 are x=(4+sqrt(19))/2 ,x=(4-sqrt(19))/2