.3t^2-24t=-240

Solution for .3t^2-24t=-240 equation:

.3t^2-24t=-240

We move all terms to the left:

.3t^2-24t-(-240)=0

We add all the numbers together, and all the variables

.3t^2-24t+240=0

a = .3; b = -24; c = +240;
Δ = b2-4ac
Δ = -242-4·.3·240
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{2}}{2*.3}=\frac{24-12\sqrt{2}}{0.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{2}}{2*.3}=\frac{24+12\sqrt{2}}{0.6}
$