0=6t^2+2t-8

Solution for 0=6t^2+2t-8 equation:

0=6t^2+2t-8

We move all terms to the left:

0-(6t^2+2t-8)=0

We add all the numbers together, and all the variables

-(6t^2+2t-8)=0

We get rid of parentheses

-6t^2-2t+8=0

a = -6; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-6)·8
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*-6}=\frac{-12}{-12}
=1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*-6}=\frac{16}{-12}
=-1+1/3
$