-5t^2-240t=1734

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

-5t^2-240t=1734

We move all terms to the left:

-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}
$