16t^2-12t=54

Solution for 16t^2-12t=54 equation:

16t^2-12t=54

We move all terms to the left:

16t^2-12t-(54)=0

a = 16; b = -12; c = -54;
Δ = b2-4ac
Δ = -122-4·16·(-54)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-60}{2*16}=\frac{-48}{32}
=-1+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+60}{2*16}=\frac{72}{32}
=2+1/4
$