(6t+8)(6t-8)=100

Solution for (6t+8)(6t-8)=100 equation:

(6t+8)(6t-8)=100

We move all terms to the left:

(6t+8)(6t-8)-(100)=0

We use the square of the difference formula

36t^2-64-100=0

We add all the numbers together, and all the variables

36t^2-164=0

a = 36; b = 0; c = -164;
Δ = b2-4ac
Δ = 02-4·36·(-164)
Δ = 23616
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:

$\sqrt{\Delta}=\sqrt{23616}=\sqrt{576*41}=\sqrt{576}*\sqrt{41}=24\sqrt{41}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{41}}{2*36}=\frac{0-24\sqrt{41}}{72}
=-\frac{24\sqrt{41}}{72}
=-\frac{\sqrt{41}}{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{41}}{2*36}=\frac{0+24\sqrt{41}}{72}
=\frac{24\sqrt{41}}{72}
=\frac{\sqrt{41}}{3}
$