100=30t+1.75t^2

Solution for 100=30t+1.75t^2 equation:

100=30t+1.75t^2

We move all terms to the left:

100-(30t+1.75t^2)=0

We get rid of parentheses

-1.75t^2-30t+100=0

a = -1.75; b = -30; c = +100;
Δ = b2-4ac
Δ = -302-4·(-1.75)·100
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-40}{2*-1.75}=\frac{-10}{-3.5}
=2+1/1.1666666666667
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+40}{2*-1.75}=\frac{70}{-3.5}
=-20
$