125=t^2

Solution for 125=t^2 equation:

125=t^2

We move all terms to the left:

125-(t^2)=0

We add all the numbers together, and all the variables

-1t^2+125=0

a = -1; b = 0; c = +125;
Δ = b2-4ac
Δ = 02-4·(-1)·125
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{5}}{2*-1}=\frac{0-10\sqrt{5}}{-2}
=-\frac{10\sqrt{5}}{-2}
=-\frac{5\sqrt{5}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{5}}{2*-1}=\frac{0+10\sqrt{5}}{-2}
=\frac{10\sqrt{5}}{-2}
=\frac{5\sqrt{5}}{-1}
$