1734=-5t^2-240t

Solution for 1734=-5t^2-240t equation:

1734=-5t^2-240t

We move all terms to the left:

1734-(-5t^2-240t)=0

We get rid of parentheses

5t^2+240t+1734=0

a = 5; b = 240; c = +1734;
Δ = b2-4ac
Δ = 2402-4·5·1734
Δ = 22920
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:

$\sqrt{\Delta}=\sqrt{22920}=\sqrt{4*5730}=\sqrt{4}*\sqrt{5730}=2\sqrt{5730}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-2\sqrt{5730}}{2*5}=\frac{-240-2\sqrt{5730}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+2\sqrt{5730}}{2*5}=\frac{-240+2\sqrt{5730}}{10}
$