2t^2-12t=12

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

2t^2-12t=12

We move all terms to the left:

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

a = 2; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·2·(-12)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*2}=\frac{12-4\sqrt{15}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*2}=\frac{12+4\sqrt{15}}{4}
$