30=-16t^2+70t+5

Solution for 30=-16t^2+70t+5 equation:

30=-16t^2+70t+5

We move all terms to the left:

30-(-16t^2+70t+5)=0

We get rid of parentheses

16t^2-70t-5+30=0

We add all the numbers together, and all the variables

16t^2-70t+25=0

a = 16; b = -70; c = +25;
Δ = b2-4ac
Δ = -702-4·16·25
Δ = 3300
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:

$\sqrt{\Delta}=\sqrt{3300}=\sqrt{100*33}=\sqrt{100}*\sqrt{33}=10\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-10\sqrt{33}}{2*16}=\frac{70-10\sqrt{33}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10\sqrt{33}}{2*16}=\frac{70+10\sqrt{33}}{32}
$