t=-5t^2-5t+180

Solution for t=-5t^2-5t+180 equation:

t=-5t^2-5t+180

We move all terms to the left:

t-(-5t^2-5t+180)=0

We get rid of parentheses

5t^2+5t+t-180=0

We add all the numbers together, and all the variables

5t^2+6t-180=0

a = 5; b = 6; c = -180;
Δ = b2-4ac
Δ = 62-4·5·(-180)
Δ = 3636
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:

$\sqrt{\Delta}=\sqrt{3636}=\sqrt{36*101}=\sqrt{36}*\sqrt{101}=6\sqrt{101}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{101}}{2*5}=\frac{-6-6\sqrt{101}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{101}}{2*5}=\frac{-6+6\sqrt{101}}{10}
$