100=3*(t*t)

Solution for 100=3*(t*t) equation:

100=3(t*t)

We move all terms to the left:

100-(3(t*t))=0

We add all the numbers together, and all the variables

-(3(+t*t))+100=0


We calculate terms in parentheses: -(3(+t*t)), so:

3(+t*t)

We multiply parentheses

3t^2

Back to the equation:

-(3t^2)


a = -3; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-3)·100
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*-3}=\frac{0-20\sqrt{3}}{-6}
=-\frac{20\sqrt{3}}{-6}
=-\frac{10\sqrt{3}}{-3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*-3}=\frac{0+20\sqrt{3}}{-6}
=\frac{20\sqrt{3}}{-6}
=\frac{10\sqrt{3}}{-3}
$