30t+5t^2=80

Solution for 30t+5t^2=80 equation:

30t+5t^2=80

We move all terms to the left:

30t+5t^2-(80)=0

a = 5; b = 30; c = -80;
Δ = b2-4ac
Δ = 302-4·5·(-80)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-50}{2*5}=\frac{-80}{10}
=-8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+50}{2*5}=\frac{20}{10}
=2
$