50t^2+1000t=20000

Solution for 50t^2+1000t=20000 equation:

50t^2+1000t=20000

We move all terms to the left:

50t^2+1000t-(20000)=0

a = 50; b = 1000; c = -20000;
Δ = b2-4ac
Δ = 10002-4·50·(-20000)
Δ = 5000000
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:

$\sqrt{\Delta}=\sqrt{5000000}=\sqrt{1000000*5}=\sqrt{1000000}*\sqrt{5}=1000\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-1000\sqrt{5}}{2*50}=\frac{-1000-1000\sqrt{5}}{100}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+1000\sqrt{5}}{2*50}=\frac{-1000+1000\sqrt{5}}{100}
$