32x^2/3=16

Solution for 32x^2/3=16 equation:

32x^2/3=16

We move all terms to the left:

32x^2/3-(16)=0

We multiply all the terms by the denominator


32x^2-16*3=0

We add all the numbers together, and all the variables

32x^2-48=0

a = 32; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·32·(-48)
Δ = 6144
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:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{6}}{2*32}=\frac{0-32\sqrt{6}}{64}
=-\frac{32\sqrt{6}}{64}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{6}}{2*32}=\frac{0+32\sqrt{6}}{64}
=\frac{32\sqrt{6}}{64}
=\frac{\sqrt{6}}{2}
$