12t+2t^2=54

Solution for 12t+2t^2=54 equation:

12t+2t^2=54

We move all terms to the left:

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

a = 2; b = 12; c = -54;
Δ = b2-4ac
Δ = 122-4·2·(-54)
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{-(12)-24}{2*2}=\frac{-36}{4}
=-9
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*2}=\frac{12}{4}
=3
$