3t^2-54t=-195

Solution for 3t^2-54t=-195 equation:

3t^2-54t=-195

We move all terms to the left:

3t^2-54t-(-195)=0

We add all the numbers together, and all the variables

3t^2-54t+195=0

a = 3; b = -54; c = +195;
Δ = b2-4ac
Δ = -542-4·3·195
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-24}{2*3}=\frac{30}{6}
=5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+24}{2*3}=\frac{78}{6}
=13
$