-15t^2+44t-24=0

Solution for -15t^2+44t-24=0 equation:

-15t^2+44t-24=0

a = -15; b = 44; c = -24;
Δ = b2-4ac
Δ = 442-4·(-15)·(-24)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{31}}{2*-15}=\frac{-44-4\sqrt{31}}{-30}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{31}}{2*-15}=\frac{-44+4\sqrt{31}}{-30}
$