0=16t^2+100t+35

Solution for 0=16t^2+100t+35 equation:

0=16t^2+100t+35

We move all terms to the left:

0-(16t^2+100t+35)=0

We add all the numbers together, and all the variables

-(16t^2+100t+35)=0

We get rid of parentheses

-16t^2-100t-35=0

a = -16; b = -100; c = -35;
Δ = b2-4ac
Δ = -1002-4·(-16)·(-35)
Δ = 7760
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:

$\sqrt{\Delta}=\sqrt{7760}=\sqrt{16*485}=\sqrt{16}*\sqrt{485}=4\sqrt{485}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{485}}{2*-16}=\frac{100-4\sqrt{485}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{485}}{2*-16}=\frac{100+4\sqrt{485}}{-32}
$