18=1/2(4t)2

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Solution for 18=1/2(4t)2 equation:



18=1/2(4t)2
We move all terms to the left:
18-(1/2(4t)2)=0
Domain of the equation: 24t2)!=0
t!=0/1
t!=0
t∈R
We add all the numbers together, and all the variables
-(+1/24t2)+18=0
We get rid of parentheses
-1/24t2+18=0
We multiply all the terms by the denominator
18*24t2-1=0
Wy multiply elements
432t^2-1=0
a = 432; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·432·(-1)
Δ = 1728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*432}=\frac{0-24\sqrt{3}}{864} =-\frac{24\sqrt{3}}{864} =-\frac{\sqrt{3}}{36} $
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*432}=\frac{0+24\sqrt{3}}{864} =\frac{24\sqrt{3}}{864} =\frac{\sqrt{3}}{36} $

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