T=20+50-16t^2

Solution for T=20+50-16t^2 equation:

=20+50-16T^2

We move all terms to the left:

-(20+50-16T^2)=0

We get rid of parentheses

16T^2-20-50=0

We add all the numbers together, and all the variables

16T^2-70=0

a = 16; b = 0; c = -70;
Δ = b2-4ac
Δ = 02-4·16·(-70)
Δ = 4480
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:

$\sqrt{\Delta}=\sqrt{4480}=\sqrt{64*70}=\sqrt{64}*\sqrt{70}=8\sqrt{70}$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{70}}{2*16}=\frac{0-8\sqrt{70}}{32}
=-\frac{8\sqrt{70}}{32}
=-\frac{\sqrt{70}}{4}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{70}}{2*16}=\frac{0+8\sqrt{70}}{32}
=\frac{8\sqrt{70}}{32}
=\frac{\sqrt{70}}{4}
$