Solve 4(2a^2) =8 (2-3a)

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

a_{1} = - \frac{3 + 17}{2}, a_{2} = \frac{- 3 + 17}{2}

Alternative Form

a_{1} \approx - 3.561553, a_{2} \approx 0.561553

Evaluate

4 \times 2 a^{2} = 8 (2 - 3 a)

Multiply the numbers

8 a^{2} = 8 (2 - 3 a)

Expand the expression

More Steps

8 a^{2} = 16 - 24 a

Move the expression to the left side

8 a^{2} - 16 + 24 a = 0

Rewrite in standard form

8 a^{2} + 24 a - 16 = 0

Substitute a= 8,b= 24 and c= - 16 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{- 24 \pm 2 4 ^{2} - 4 \times 8 ( - 16 )}{2 \times 8}

Simplify the expression

a = \frac{- 24 \pm 2 4 ^{2} - 4 \times 8 ( - 16 )}{16}

Simplify the expression

More Steps

a = \frac{- 24 \pm 1088}{16}

Simplify the radical expression

More Steps

a = \frac{- 24 \pm 8 17}{16}

Separate the equation into 2 possible cases

a = \frac{- 24 + 8 17}{16} a = \frac{- 24 - 8 17}{16}

Simplify the expression

More Steps

a = \frac{- 3 + 17}{2} a = \frac{- 24 - 8 17}{16}

Simplify the expression

More Steps

a = \frac{- 3 + 17}{2} a = - \frac{3 + 17}{2}

Solution

a_{1} = - \frac{3 + 17}{2}, a_{2} = \frac{- 3 + 17}{2}

Alternative Form

a_{1} \approx - 3.561553, a_{2} \approx 0.561553

Show Solution