486=1/2*3x*x

Solution for 486=1/2*3x*x equation:

486=1/2*3x*x

We move all terms to the left:

486-(1/2*3x*x)=0


Domain of the equation: 2*3x*x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+1/2*3x*x)+486=0

We get rid of parentheses

-1/2*3x*x+486=0

We multiply all the terms by the denominator


486*2*3x*x-1=0

Wy multiply elements

2916x^2*3-1=0

Wy multiply elements

8748x^2-1=0

a = 8748; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·8748·(-1)
Δ = 34992
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:

$\sqrt{\Delta}=\sqrt{34992}=\sqrt{11664*3}=\sqrt{11664}*\sqrt{3}=108\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108\sqrt{3}}{2*8748}=\frac{0-108\sqrt{3}}{17496}
=-\frac{108\sqrt{3}}{17496}
=-\frac{\sqrt{3}}{162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108\sqrt{3}}{2*8748}=\frac{0+108\sqrt{3}}{17496}
=\frac{108\sqrt{3}}{17496}
=\frac{\sqrt{3}}{162}
$