30t-10t^2+100=0

Solution for 30t-10t^2+100=0 equation:

30t-10t^2+100=0

a = -10; b = 30; c = +100;
Δ = b2-4ac
Δ = 302-4·(-10)·100
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-70}{2*-10}=\frac{-100}{-20}
=+5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+70}{2*-10}=\frac{40}{-20}
=-2
$