-1.86t^2+13t-11.14=0

Solution for -1.86t^2+13t-11.14=0 equation:

-1.86t^2+13t-11.14=0

a = -1.86; b = 13; c = -11.14;
Δ = b2-4ac
Δ = 132-4·(-1.86)·(-11.14)
Δ = 86.1184
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{-(13)-\sqrt{86.1184}}{2*-1.86}=\frac{-13-\sqrt{86.1184}}{-3.72}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{86.1184}}{2*-1.86}=\frac{-13+\sqrt{86.1184}}{-3.72}
$