4x^2/3=64

Solution for 4x^2/3=64 equation:

4x^2/3=64

We move all terms to the left:

4x^2/3-(64)=0

We multiply all the terms by the denominator


4x^2-64*3=0

We add all the numbers together, and all the variables

4x^2-192=0

a = 4; b = 0; c = -192;
Δ = b2-4ac
Δ = 02-4·4·(-192)
Δ = 3072
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{3}}{2*4}=\frac{0-32\sqrt{3}}{8}
=-\frac{32\sqrt{3}}{8}
=-4\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{3}}{2*4}=\frac{0+32\sqrt{3}}{8}
=\frac{32\sqrt{3}}{8}
=4\sqrt{3}
$