3f*f/2=486^2

Solution for 3f*f/2=486^2 equation:

3f*f/2=486^2

We move all terms to the left:

3f*f/2-(486^2)=0

We add all the numbers together, and all the variables

3f*f/2-236196=0

We multiply all the terms by the denominator


3f*f-236196*2=0

We add all the numbers together, and all the variables

3f*f-472392=0

Wy multiply elements

3f^2-472392=0

a = 3; b = 0; c = -472392;
Δ = b2-4ac
Δ = 02-4·3·(-472392)
Δ = 5668704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5668704}=\sqrt{944784*6}=\sqrt{944784}*\sqrt{6}=972\sqrt{6}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-972\sqrt{6}}{2*3}=\frac{0-972\sqrt{6}}{6}
=-\frac{972\sqrt{6}}{6}
=-162\sqrt{6}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+972\sqrt{6}}{2*3}=\frac{0+972\sqrt{6}}{6}
=\frac{972\sqrt{6}}{6}
=162\sqrt{6}
$