0=50-10-5t^2

Solution for 0=50-10-5t^2 equation:

0=50-10-5t^2

We move all terms to the left:

0-(50-10-5t^2)=0

We add all the numbers together, and all the variables

-(50-10-5t^2)=0

We get rid of parentheses

5t^2-50+10=0

We add all the numbers together, and all the variables

5t^2-40=0

a = 5; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·5·(-40)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*5}=\frac{0-20\sqrt{2}}{10}
=-\frac{20\sqrt{2}}{10}
=-2\sqrt{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*5}=\frac{0+20\sqrt{2}}{10}
=\frac{20\sqrt{2}}{10}
=2\sqrt{2}
$