12t^2-120t+10=0

Solution for 12t^2-120t+10=0 equation:

12t^2-120t+10=0

a = 12; b = -120; c = +10;
Δ = b2-4ac
Δ = -1202-4·12·10
Δ = 13920
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:

$\sqrt{\Delta}=\sqrt{13920}=\sqrt{16*870}=\sqrt{16}*\sqrt{870}=4\sqrt{870}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{870}}{2*12}=\frac{120-4\sqrt{870}}{24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{870}}{2*12}=\frac{120+4\sqrt{870}}{24}
$