216=8/3t^2

Solution for 216=8/3t^2 equation:

216=8/3t^2

We move all terms to the left:

216-(8/3t^2)=0


Domain of the equation: 3t^2)!=0

t!=0/1

t!=0

t∈R


We get rid of parentheses

-8/3t^2+216=0

We multiply all the terms by the denominator


216*3t^2-8=0

Wy multiply elements

648t^2-8=0

a = 648; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·648·(-8)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144}{2*648}=\frac{-144}{1296}
=-1/9
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144}{2*648}=\frac{144}{1296}
=1/9
$