-16t^2+70t+5=40

Solution for -16t^2+70t+5=40 equation:

-16t^2+70t+5=40

We move all terms to the left:

-16t^2+70t+5-(40)=0

We add all the numbers together, and all the variables

-16t^2+70t-35=0

a = -16; b = 70; c = -35;
Δ = b2-4ac
Δ = 702-4·(-16)·(-35)
Δ = 2660
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:

$\sqrt{\Delta}=\sqrt{2660}=\sqrt{4*665}=\sqrt{4}*\sqrt{665}=2\sqrt{665}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{665}}{2*-16}=\frac{-70-2\sqrt{665}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{665}}{2*-16}=\frac{-70+2\sqrt{665}}{-32}
$