How do you find the solution to the quadratic equation 3x^2-8=0?

1 Answer
May 13, 2015

Transposing 8 to the other side, we get:

3x^2 = 8

Dividing both sides by 3, we get:

(cancel(3)x^2)/cancel(3) = 8/3

x^2 = 8/3

Taking square root on both sides gives us:

sqrt(x^2) = sqrt(8/3)

x = +-sqrt8/sqrt3

x = +-(2sqrt2)/sqrt3

To rationalise the denominator,

x = +- ((2sqrt2)/sqrt3)*(sqrt3/sqrt3)

x = +- (2sqrt2*sqrt3)/3

We know that color(blue)(sqrta*sqrtb = sqrt(ab)

Hence x = +- (2sqrt(2*3))/3

color(green)( x = (2sqrt6)/3,-(2sqrt6)/3