Solve 4a^2-8a-1=0

Evaluate

4 a^{2} - 8 a - 1 = 0

Substitute a= 4,b= - 8 and c= - 1 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 4 ( - 1 )}{2 \times 4}

Simplify the expression

a = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 4 ( - 1 )}{8}

Simplify the expression

More Steps

a = \frac{8 \pm 80}{8}

Simplify the radical expression

More Steps

a = \frac{8 \pm 4 5}{8}

Separate the equation into 2 possible cases

a = \frac{8 + 4 5}{8} a = \frac{8 - 4 5}{8}

Simplify the expression

More Steps

a = \frac{2 + 5}{2} a = \frac{8 - 4 5}{8}

Simplify the expression

More Steps

a = \frac{2 + 5}{2} a = \frac{2 - 5}{2}

Solution

a_{1} = \frac{2 - 5}{2}, a_{2} = \frac{2 + 5}{2}

Alternative Form

a_{1} \approx - 0.118034, a_{2} \approx 2.118034

Solve the quadratic equation