Solve 11z^2-z-3=0

Evaluate

11 z^{2} - z - 3 = 0

Substitute a= 11,b= - 1 and c= - 3 into the quadratic formula z = \frac{- b \pm b ^{2} - 4 a c}{2 a}

z = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 11 ( - 3 )}{2 \times 11}

Simplify the expression

z = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 11 ( - 3 )}{22}

Simplify the expression

More Steps

z = \frac{1 \pm 133}{22}

Separate the equation into 2 possible cases

z = \frac{1 + 133}{22} z = \frac{1 - 133}{22}

Solution

z_{1} = \frac{1 - 133}{22}, z_{2} = \frac{1 + 133}{22}

Alternative Form

z_{1} \approx - 0.478753, z_{2} \approx 0.569662

Solve the quadratic equation