0=-16t^2+70t+90

Solution for 0=-16t^2+70t+90 equation:

0=-16t^2+70t+90

We move all terms to the left:

0-(-16t^2+70t+90)=0

We add all the numbers together, and all the variables

-(-16t^2+70t+90)=0

We get rid of parentheses

16t^2-70t-90=0

a = 16; b = -70; c = -90;
Δ = b2-4ac
Δ = -702-4·16·(-90)
Δ = 10660
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:

$\sqrt{\Delta}=\sqrt{10660}=\sqrt{4*2665}=\sqrt{4}*\sqrt{2665}=2\sqrt{2665}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{2665}}{2*16}=\frac{70-2\sqrt{2665}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{2665}}{2*16}=\frac{70+2\sqrt{2665}}{32}
$