6t^2-10t=-2

Solution for 6t^2-10t=-2 equation:

6t^2-10t=-2

We move all terms to the left:

6t^2-10t-(-2)=0

We add all the numbers together, and all the variables

6t^2-10t+2=0

a = 6; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·6·2
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{13}}{2*6}=\frac{10-2\sqrt{13}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{13}}{2*6}=\frac{10+2\sqrt{13}}{12}
$