Solve 12x^2 - 8x - 11

Question

Find the roots

x_{1} = \frac{2 - 37}{6}, x_{2} = \frac{2 + 37}{6}

Alternative Form

x_{1} \approx - 0.68046, x_{2} \approx 1.347127

Evaluate

12 x^{2} - 8 x - 11

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

12 x^{2} - 8 x - 11 = 0

Substitute a= 12,b= - 8 and c= - 11 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 12 ( - 11 )}{2 \times 12}

Simplify the expression

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 12 ( - 11 )}{24}

Simplify the expression

More Steps

x = \frac{8 \pm 592}{24}

Simplify the radical expression

More Steps

x = \frac{8 \pm 4 37}{24}

Separate the equation into 2 possible cases

x = \frac{8 + 4 37}{24} x = \frac{8 - 4 37}{24}

Simplify the expression

More Steps

x = \frac{2 + 37}{6} x = \frac{8 - 4 37}{24}

Simplify the expression

More Steps

x = \frac{2 + 37}{6} x = \frac{2 - 37}{6}

Solution

x_{1} = \frac{2 - 37}{6}, x_{2} = \frac{2 + 37}{6}

Alternative Form

x_{1} \approx - 0.68046, x_{2} \approx 1.347127

Show Solution