18=1/2(4t)2

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}
$