150(1600-800t+t^2)=0

Solution for 150(1600-800t+t^2)=0 equation:

150(1600-800t+t^2)=0

We multiply parentheses

150t^2-120000t+240000=0

a = 150; b = -120000; c = +240000;
Δ = b2-4ac
Δ = -1200002-4·150·240000
Δ = 14256000000
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:

$\sqrt{\Delta}=\sqrt{14256000000}=\sqrt{1296000000*11}=\sqrt{1296000000}*\sqrt{11}=36000\sqrt{11}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120000)-36000\sqrt{11}}{2*150}=\frac{120000-36000\sqrt{11}}{300}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120000)+36000\sqrt{11}}{2*150}=\frac{120000+36000\sqrt{11}}{300}
$