-5.1t^2-5t+60=0

Solution for -5.1t^2-5t+60=0 equation:

-5.1t^2-5t+60=0

a = -5.1; b = -5; c = +60;
Δ = b2-4ac
Δ = -52-4·(-5.1)·60
Δ = 1249
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{-(-5)-\sqrt{1249}}{2*-5.1}=\frac{5-\sqrt{1249}}{-10.2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{1249}}{2*-5.1}=\frac{5+\sqrt{1249}}{-10.2}
$