Solve 3x^2-12x-1=0

Evaluate

3 x^{2} - 12 x - 1 = 0

Substitute a= 3,b= - 12 and c= - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 3 ( - 1 )}{2 \times 3}

Simplify the expression

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 3 ( - 1 )}{6}

Simplify the expression

More Steps

x = \frac{12 \pm 156}{6}

Simplify the radical expression

More Steps

x = \frac{12 \pm 2 39}{6}

Separate the equation into 2 possible cases

x = \frac{12 + 2 39}{6} x = \frac{12 - 2 39}{6}

Simplify the expression

More Steps

x = \frac{6 + 39}{3} x = \frac{12 - 2 39}{6}

Simplify the expression

More Steps

x = \frac{6 + 39}{3} x = \frac{6 - 39}{3}

Solution

x_{1} = \frac{6 - 39}{3}, x_{2} = \frac{6 + 39}{3}

Alternative Form

x_{1} \approx - 0.081666, x_{2} \approx 4.081666

Solve the quadratic equation