-3x^2 + 4 = 0
subtract 4 from both sides
-3x^2 + 4 - 4 = 0 - 4
-3x^2 = -4
divide by -3 on both sides
-3x^2 / -3 = -4 / -3
x^2 = 4/3
square root of both sides
x = +- sqrt(4/3)
Note: The +- is because numbers have negative and positive square roots, like how the square roots of 25 are -5 and +5 because -5 * -5 = 25 and +5 * +5 = 25. The +- means we'll get two different answers that are both true.
x = +- 2 / sqrt(3)
There's a thing I don't think I can explain adequately, but we don't like square roots on the bottom if we can help it. Since 1 / sqrt(3) = sqrt(3) / 3 we can do this:
x = +- 2 ( sqrt(3) / 3 )
x = +- 2sqrt(3)/3
x = -2sqrt(3)/3 or x = 2sqrt(3)/3