(6t-4)(6t-4)=6

Solution for (6t-4)(6t-4)=6 equation:

(6t-4)(6t-4)=6

We move all terms to the left:

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

We multiply parentheses ..

(+36t^2-24t-24t+16)-6=0

We get rid of parentheses

36t^2-24t-24t+16-6=0

We add all the numbers together, and all the variables

36t^2-48t+10=0

a = 36; b = -48; c = +10;
Δ = b2-4ac
Δ = -482-4·36·10
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{6}}{2*36}=\frac{48-12\sqrt{6}}{72}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{6}}{2*36}=\frac{48+12\sqrt{6}}{72}
$