Solve 2(d-3) 3d =9

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

d_{1} = \frac{3 - 15}{2}, d_{2} = \frac{3 + 15}{2}

Alternative Form

d_{1} \approx - 0.436492, d_{2} \approx 3.436492

Evaluate

2 (d - 3) \times 3 d = 9

Multiply

More Steps

6 d (d - 3) = 9

Expand the expression

More Steps

6 d^{2} - 18 d = 9

Move the expression to the left side

6 d^{2} - 18 d - 9 = 0

Substitute a= 6,b= - 18 and c= - 9 into the quadratic formula d = \frac{- b \pm b ^{2} - 4 a c}{2 a}

d = \frac{18 \pm ( - 18 ) ^{2} - 4 \times 6 ( - 9 )}{2 \times 6}

Simplify the expression

d = \frac{18 \pm ( - 18 ) ^{2} - 4 \times 6 ( - 9 )}{12}

Simplify the expression

More Steps

d = \frac{18 \pm 540}{12}

Simplify the radical expression

More Steps

d = \frac{18 \pm 6 15}{12}

Separate the equation into 2 possible cases

d = \frac{18 + 6 15}{12} d = \frac{18 - 6 15}{12}

Simplify the expression

More Steps

d = \frac{3 + 15}{2} d = \frac{18 - 6 15}{12}

Simplify the expression

More Steps

d = \frac{3 + 15}{2} d = \frac{3 - 15}{2}

Solution

d_{1} = \frac{3 - 15}{2}, d_{2} = \frac{3 + 15}{2}

Alternative Form

d_{1} \approx - 0.436492, d_{2} \approx 3.436492

Show Solution