4t(t-6)=24

Solution for 4t(t-6)=24 equation:

4t(t-6)=24

We move all terms to the left:

4t(t-6)-(24)=0

We multiply parentheses

4t^2-24t-24=0

a = 4; b = -24; c = -24;
Δ = b2-4ac
Δ = -242-4·4·(-24)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{15}}{2*4}=\frac{24-8\sqrt{15}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{15}}{2*4}=\frac{24+8\sqrt{15}}{8}
$