Solve 48x ^ 2 - 40x - 1

Question

Find the roots

x_{1} = \frac{5 - 2 7}{12}, x_{2} = \frac{5 + 2 7}{12}

Alternative Form

x_{1} \approx - 0.024292, x_{2} \approx 0.857625

Evaluate

48 x^{2} - 40 x - 1

To find the roots of the expression,set the expression equal to 0

48 x^{2} - 40 x - 1 = 0

Substitute a= 48,b= - 40 and c= - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{40 \pm ( - 40 ) ^{2} - 4 \times 48 ( - 1 )}{2 \times 48}

Simplify the expression

x = \frac{40 \pm ( - 40 ) ^{2} - 4 \times 48 ( - 1 )}{96}

Simplify the expression

More Steps

x = \frac{40 \pm 1792}{96}

Simplify the radical expression

More Steps

x = \frac{40 \pm 16 7}{96}

Separate the equation into 2 possible cases

x = \frac{40 + 16 7}{96} x = \frac{40 - 16 7}{96}

Simplify the expression

More Steps

x = \frac{5 + 2 7}{12} x = \frac{40 - 16 7}{96}

Simplify the expression

More Steps

x = \frac{5 + 2 7}{12} x = \frac{5 - 2 7}{12}

Solution

x_{1} = \frac{5 - 2 7}{12}, x_{2} = \frac{5 + 2 7}{12}

Alternative Form

x_{1} \approx - 0.024292, x_{2} \approx 0.857625

Show Solution