Solve 3y^2 - 18y - 5 = 0

Evaluate

3 y^{2} - 18 y - 5 = 0

Substitute a= 3,b= - 18 and c= - 5 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{18 \pm ( - 18 ) ^{2} - 4 \times 3 ( - 5 )}{2 \times 3}

Simplify the expression

y = \frac{18 \pm ( - 18 ) ^{2} - 4 \times 3 ( - 5 )}{6}

Simplify the expression

More Steps

y = \frac{18 \pm 384}{6}

Simplify the radical expression

More Steps

y = \frac{18 \pm 8 6}{6}

Separate the equation into 2 possible cases

y = \frac{18 + 8 6}{6} y = \frac{18 - 8 6}{6}

Simplify the expression

More Steps

y = \frac{9 + 4 6}{3} y = \frac{18 - 8 6}{6}

Simplify the expression

More Steps

y = \frac{9 + 4 6}{3} y = \frac{9 - 4 6}{3}

Solution

y_{1} = \frac{9 - 4 6}{3}, y_{2} = \frac{9 + 4 6}{3}

Alternative Form

y_{1} \approx - 0.265986, y_{2} \approx 6.265986

Solve the quadratic equation