Question

A^2(64a^2-3)/3=27-4a^2/4

Answer 1

The answer is a = 3/4 = 0.75

First get rid of the paranthesis,
${a}^{2} (64 {a}^{2} - 3) = 64 {a}^{4} - 3 {a}^{2}$
Then set the denominators equal:
$\frac{ 256 {a}^{4} - 12 {a}^{2}}{12} = \frac{81 - 12 {a}^{2} }{12}$
Then remove the denominators and solve:
$256 {a}^{4} - 12 {a}^{2} = 81 - 12 {a}^{2}$
Eliminate -12a^2 by adding 12a^2 to both sides:
$256 {a}^{4} = 81$
Take the fourth root of them or take the square root twice:
$\sqrt[4]{256 {a}^{4} } = \sqrt[4]{81} \\ 4a = 3$
Divide both sides by 4:
$a = \frac{3}{4} = 0.75$