0=5t^2-10t-5

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

0=5t^2-10t-5

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -5; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·(-5)·5
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{2}}{2*-5}=\frac{-10-10\sqrt{2}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{2}}{2*-5}=\frac{-10+10\sqrt{2}}{-10}
$