125=5t+5t^2

Solution for 125=5t+5t^2 equation:

125=5t+5t^2

We move all terms to the left:

125-(5t+5t^2)=0

We get rid of parentheses

-5t^2-5t+125=0

a = -5; b = -5; c = +125;
Δ = b2-4ac
Δ = -52-4·(-5)·125
Δ = 2525
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:

$\sqrt{\Delta}=\sqrt{2525}=\sqrt{25*101}=\sqrt{25}*\sqrt{101}=5\sqrt{101}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{101}}{2*-5}=\frac{5-5\sqrt{101}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{101}}{2*-5}=\frac{5+5\sqrt{101}}{-10}
$