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

May 13, 2015

Transposing $8$ to the other side, we get:

$3 {x}^{2} = 8$

Dividing both sides by 3, we get:

$\frac{\cancel{3} {x}^{2}}{\cancel{3}} = \frac{8}{3}$

${x}^{2} = \frac{8}{3}$

Taking square root on both sides gives us:

$\sqrt{{x}^{2}} = \sqrt{\frac{8}{3}}$

$x = \pm \frac{\sqrt{8}}{\sqrt{3}}$

$x = \pm \frac{2 \sqrt{2}}{\sqrt{3}}$

To rationalise the denominator,

$x = \pm \left(\frac{2 \sqrt{2}}{\sqrt{3}}\right) \cdot \left(\frac{\sqrt{3}}{\sqrt{3}}\right)$

$x = \pm \frac{2 \sqrt{2} \cdot \sqrt{3}}{3}$

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

Hence $x = \pm \frac{2 \sqrt{2 \cdot 3}}{3}$

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