x^2=16/32

Solution for x^2=16/32 equation:

x^2=16/32

We move all terms to the left:

x^2-(16/32)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

x^2-16/32=0

We multiply all the terms by the denominator


x^2*32-16=0

Wy multiply elements

32x^2-16=0

a = 32; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·32·(-16)
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{2}}{2*32}=\frac{0-32\sqrt{2}}{64}
=-\frac{32\sqrt{2}}{64}
=-\frac{\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{2}}{2*32}=\frac{0+32\sqrt{2}}{64}
=\frac{32\sqrt{2}}{64}
=\frac{\sqrt{2}}{2}
$