(7t-7)(7t-7)=7

Solution for (7t-7)(7t-7)=7 equation:

(7t-7)(7t-7)=7

We move all terms to the left:

(7t-7)(7t-7)-(7)=0

We multiply parentheses ..

(+49t^2-49t-49t+49)-7=0

We get rid of parentheses

49t^2-49t-49t+49-7=0

We add all the numbers together, and all the variables

49t^2-98t+42=0

a = 49; b = -98; c = +42;
Δ = b2-4ac
Δ = -982-4·49·42
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-14\sqrt{7}}{2*49}=\frac{98-14\sqrt{7}}{98}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+14\sqrt{7}}{2*49}=\frac{98+14\sqrt{7}}{98}
$