Solve -6x^2 - 2 - 3x = -8

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = - \frac{1 + 17}{4}, x_{2} = \frac{- 1 + 17}{4}

Alternative Form

x_{1} \approx - 1.280776, x_{2} \approx 0.780776

Evaluate

- 6 x^{2} - 2 - 3 x = - 8

Move the expression to the left side

- 6 x^{2} + 6 - 3 x = 0

Rewrite in standard form

- 6 x^{2} - 3 x + 6 = 0

Multiply both sides

6 x^{2} + 3 x - 6 = 0

Substitute a= 6,b= 3 and c= - 6 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

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

Simplify the expression

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

Simplify the expression

More Steps

x = \frac{- 3 \pm 153}{12}

Simplify the radical expression

More Steps

x = \frac{- 3 \pm 3 17}{12}

Separate the equation into 2 possible cases

x = \frac{- 3 + 3 17}{12} x = \frac{- 3 - 3 17}{12}

Simplify the expression

More Steps

x = \frac{- 1 + 17}{4} x = \frac{- 3 - 3 17}{12}

Simplify the expression

More Steps

x = \frac{- 1 + 17}{4} x = - \frac{1 + 17}{4}

Solution

x_{1} = - \frac{1 + 17}{4}, x_{2} = \frac{- 1 + 17}{4}

Alternative Form

x_{1} \approx - 1.280776, x_{2} \approx 0.780776

Show Solution