t=-13t^2+120t+8

Solution for t=-13t^2+120t+8 equation:

t=-13t^2+120t+8

We move all terms to the left:

t-(-13t^2+120t+8)=0

We get rid of parentheses

13t^2-120t+t-8=0

We add all the numbers together, and all the variables

13t^2-119t-8=0

a = 13; b = -119; c = -8;
Δ = b2-4ac
Δ = -1192-4·13·(-8)
Δ = 14577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-\sqrt{14577}}{2*13}=\frac{119-\sqrt{14577}}{26}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+\sqrt{14577}}{2*13}=\frac{119+\sqrt{14577}}{26}
$