3t2=3(5)2=

Solution for 3t2=3(5)2= equation:

3t^2=3(5)2=

We move all terms to the left:

3t^2-(3(5)2)=0

determiningTheFunctionDomain
3t^2-352=0

a = 3; b = 0; c = -352;
Δ = b2-4ac
Δ = 02-4·3·(-352)
Δ = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{66}}{2*3}=\frac{0-8\sqrt{66}}{6}
=-\frac{8\sqrt{66}}{6}
=-\frac{4\sqrt{66}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{66}}{2*3}=\frac{0+8\sqrt{66}}{6}
=\frac{8\sqrt{66}}{6}
=\frac{4\sqrt{66}}{3}
$