0=5t^2+10t-40

Solution for 0=5t^2+10t-40 equation:

0=5t^2+10t-40

We move all terms to the left:

0-(5t^2+10t-40)=0

We add all the numbers together, and all the variables

-(5t^2+10t-40)=0

We get rid of parentheses

-5t^2-10t+40=0

a = -5; b = -10; c = +40;
Δ = b2-4ac
Δ = -102-4·(-5)·40
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30}{2*-5}=\frac{-20}{-10}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30}{2*-5}=\frac{40}{-10}
=-4
$