500=50t+t^2

Solution for 500=50t+t^2 equation:

500=50t+t^2

We move all terms to the left:

500-(50t+t^2)=0

We get rid of parentheses

-t^2-50t+500=0

We add all the numbers together, and all the variables

-1t^2-50t+500=0

a = -1; b = -50; c = +500;
Δ = b2-4ac
Δ = -502-4·(-1)·500
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-30\sqrt{5}}{2*-1}=\frac{50-30\sqrt{5}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+30\sqrt{5}}{2*-1}=\frac{50+30\sqrt{5}}{-2}
$