x^2/4=32

Solution for x^2/4=32 equation:

x^2/4=32

We move all terms to the left:

x^2/4-(32)=0

We multiply all the terms by the denominator


x^2-32*4=0

We add all the numbers together, and all the variables

x^2-128=0

a = 1; b = 0; c = -128;
Δ = b2-4ac
Δ = 02-4·1·(-128)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{2}}{2*1}=\frac{0-16\sqrt{2}}{2}
=-\frac{16\sqrt{2}}{2}
=-8\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{2}}{2*1}=\frac{0+16\sqrt{2}}{2}
=\frac{16\sqrt{2}}{2}
=8\sqrt{2}
$