8t^2-61t-24=0

Solution for 8t^2-61t-24=0 equation:

8t^2-61t-24=0

a = 8; b = -61; c = -24;
Δ = b2-4ac
Δ = -612-4·8·(-24)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-67}{2*8}=\frac{-6}{16}
=-3/8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+67}{2*8}=\frac{128}{16}
=8
$