10=-16t^2+70t+50

Solution for 10=-16t^2+70t+50 equation:

10=-16t^2+70t+50

We move all terms to the left:

10-(-16t^2+70t+50)=0

We get rid of parentheses

16t^2-70t-50+10=0

We add all the numbers together, and all the variables

16t^2-70t-40=0

a = 16; b = -70; c = -40;
Δ = b2-4ac
Δ = -702-4·16·(-40)
Δ = 7460
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:

$\sqrt{\Delta}=\sqrt{7460}=\sqrt{4*1865}=\sqrt{4}*\sqrt{1865}=2\sqrt{1865}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1865}}{2*16}=\frac{70-2\sqrt{1865}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1865}}{2*16}=\frac{70+2\sqrt{1865}}{32}
$