88-24t-0.5(t^2)=0

Solution for 88-24t-0.5(t^2)=0 equation:

88-24t-0.5(t^2)=0

determiningTheFunctionDomain
-0.5t^2-24t+88=0

a = -0.5; b = -24; c = +88;
Δ = b2-4ac
Δ = -242-4·(-0.5)·88
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{47}}{2*-0.5}=\frac{24-4\sqrt{47}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{47}}{2*-0.5}=\frac{24+4\sqrt{47}}{-1}
$