4=6t^2-2t

Solution for 4=6t^2-2t equation:

4=6t^2-2t

We move all terms to the left:

4-(6t^2-2t)=0

We get rid of parentheses

-6t^2+2t+4=0

a = -6; b = 2; c = +4;
Δ = b2-4ac
Δ = 22-4·(-6)·4
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*-6}=\frac{-12}{-12}
=1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*-6}=\frac{8}{-12}
=-2/3
$