Solve 12h=5-3h^2 - ScanMath

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

h_{1} = - \frac{6 + 51}{3}, h_{2} = \frac{- 6 + 51}{3}

Alternative Form

h_{1} \approx - 4.380476, h_{2} \approx 0.380476

Evaluate

12 h = 5 - 3 h^{2}

Swap the sides

5 - 3 h^{2} = 12 h

Move the expression to the left side

5 - 3 h^{2} - 12 h = 0

Rewrite in standard form

- 3 h^{2} - 12 h + 5 = 0

Multiply both sides

3 h^{2} + 12 h - 5 = 0

Substitute a= 3,b= 12 and c= - 5 into the quadratic formula h = \frac{- b \pm b ^{2} - 4 a c}{2 a}

h = \frac{- 12 \pm 1 2 ^{2} - 4 \times 3 ( - 5 )}{2 \times 3}

Simplify the expression

h = \frac{- 12 \pm 1 2 ^{2} - 4 \times 3 ( - 5 )}{6}

Simplify the expression

More Steps

h = \frac{- 12 \pm 204}{6}

Simplify the radical expression

More Steps

h = \frac{- 12 \pm 2 51}{6}

Separate the equation into 2 possible cases

h = \frac{- 12 + 2 51}{6} h = \frac{- 12 - 2 51}{6}

Simplify the expression

More Steps

h = \frac{- 6 + 51}{3} h = \frac{- 12 - 2 51}{6}

Simplify the expression

More Steps

h = \frac{- 6 + 51}{3} h = - \frac{6 + 51}{3}

Solution

h_{1} = - \frac{6 + 51}{3}, h_{2} = \frac{- 6 + 51}{3}

Alternative Form

h_{1} \approx - 4.380476, h_{2} \approx 0.380476

Show Solution