5+50t+16t2=50

Solution for 5+50t+16t2=50 equation:

5+50t+16t^2=50

We move all terms to the left:

5+50t+16t^2-(50)=0

We add all the numbers together, and all the variables

16t^2+50t-45=0

a = 16; b = 50; c = -45;
Δ = b2-4ac
Δ = 502-4·16·(-45)
Δ = 5380
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:

$\sqrt{\Delta}=\sqrt{5380}=\sqrt{4*1345}=\sqrt{4}*\sqrt{1345}=2\sqrt{1345}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{1345}}{2*16}=\frac{-50-2\sqrt{1345}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{1345}}{2*16}=\frac{-50+2\sqrt{1345}}{32}
$