-5t^2+30t+60=20

Solution for -5t^2+30t+60=20 equation:

-5t^2+30t+60=20

We move all terms to the left:

-5t^2+30t+60-(20)=0

We add all the numbers together, and all the variables

-5t^2+30t+40=0

a = -5; b = 30; c = +40;
Δ = b2-4ac
Δ = 302-4·(-5)·40
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{17}}{2*-5}=\frac{-30-10\sqrt{17}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{17}}{2*-5}=\frac{-30+10\sqrt{17}}{-10}
$