0=40t+10t^2-240

Solution for 0=40t+10t^2-240 equation:

0=40t+10t^2-240

We move all terms to the left:

0-(40t+10t^2-240)=0

We add all the numbers together, and all the variables

-(40t+10t^2-240)=0

We get rid of parentheses

-10t^2-40t+240=0

a = -10; b = -40; c = +240;
Δ = b2-4ac
Δ = -402-4·(-10)·240
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40\sqrt{7}}{2*-10}=\frac{40-40\sqrt{7}}{-20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40\sqrt{7}}{2*-10}=\frac{40+40\sqrt{7}}{-20}
$