7t^2-7=7t

Solution for 7t^2-7=7t equation:

7t^2-7=7t

We move all terms to the left:

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

a = 7; b = -7; c = -7;
Δ = b2-4ac
Δ = -72-4·7·(-7)
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7\sqrt{5}}{2*7}=\frac{7-7\sqrt{5}}{14}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7\sqrt{5}}{2*7}=\frac{7+7\sqrt{5}}{14}
$