10=-5t^2-10t+250

Solution for 10=-5t^2-10t+250 equation:

10=-5t^2-10t+250

We move all terms to the left:

10-(-5t^2-10t+250)=0

We get rid of parentheses

5t^2+10t-250+10=0

We add all the numbers together, and all the variables

5t^2+10t-240=0

a = 5; b = 10; c = -240;
Δ = b2-4ac
Δ = 102-4·5·(-240)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-70}{2*5}=\frac{-80}{10}
=-8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+70}{2*5}=\frac{60}{10}
=6
$