Solve -3x^2-24x 17=-40

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = - \frac{204 + 2 10434}{3}, x_{2} = \frac{- 204 + 2 10434}{3}

Alternative Form

x_{1} \approx - 136.097969, x_{2} \approx 0.097969

Evaluate

- 3 x^{2} - 24 x \times 17 = - 40

Multiply the terms

- 3 x^{2} - 408 x = - 40

Move the expression to the left side

- 3 x^{2} - 408 x + 40 = 0

Multiply both sides

3 x^{2} + 408 x - 40 = 0

Substitute a= 3,b= 408 and c= - 40 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 408 \pm 40 8 ^{2} - 4 \times 3 ( - 40 )}{2 \times 3}

Simplify the expression

x = \frac{- 408 \pm 40 8 ^{2} - 4 \times 3 ( - 40 )}{6}

Simplify the expression

More Steps

x = \frac{- 408 \pm 40 8 ^{2} + 480}{6}

Simplify the radical expression

More Steps

x = \frac{- 408 \pm 4 10434}{6}

Separate the equation into 2 possible cases

x = \frac{- 408 + 4 10434}{6} x = \frac{- 408 - 4 10434}{6}

Simplify the expression

More Steps

x = \frac{- 204 + 2 10434}{3} x = \frac{- 408 - 4 10434}{6}

Simplify the expression

More Steps

x = \frac{- 204 + 2 10434}{3} x = - \frac{204 + 2 10434}{3}

Solution

x_{1} = - \frac{204 + 2 10434}{3}, x_{2} = \frac{- 204 + 2 10434}{3}

Alternative Form

x_{1} \approx - 136.097969, x_{2} \approx 0.097969

Show Solution