12.5=t^2-2t

Solution for 12.5=t^2-2t equation:

12.5=t^2-2t

We move all terms to the left:

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

We get rid of parentheses

-t^2+2t+12.5=0

We add all the numbers together, and all the variables

-1t^2+2t+12.5=0

a = -1; b = 2; c = +12.5;
Δ = b2-4ac
Δ = 22-4·(-1)·12.5
Δ = 54
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:

$\sqrt{\Delta}=\sqrt{54}=\sqrt{9*6}=\sqrt{9}*\sqrt{6}=3\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-3\sqrt{6}}{2*-1}=\frac{-2-3\sqrt{6}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+3\sqrt{6}}{2*-1}=\frac{-2+3\sqrt{6}}{-2}
$