-35=-5t^2+8t

Solution for -35=-5t^2+8t equation:

-35=-5t^2+8t

We move all terms to the left:

-35-(-5t^2+8t)=0

We get rid of parentheses

5t^2-8t-35=0

a = 5; b = -8; c = -35;
Δ = b2-4ac
Δ = -82-4·5·(-35)
Δ = 764
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:

$\sqrt{\Delta}=\sqrt{764}=\sqrt{4*191}=\sqrt{4}*\sqrt{191}=2\sqrt{191}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{191}}{2*5}=\frac{8-2\sqrt{191}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{191}}{2*5}=\frac{8+2\sqrt{191}}{10}
$