25t^2=50t+25

Solution for 25t^2=50t+25 equation:

25t^2=50t+25

We move all terms to the left:

25t^2-(50t+25)=0

We get rid of parentheses

25t^2-50t-25=0

a = 25; b = -50; c = -25;
Δ = b2-4ac
Δ = -502-4·25·(-25)
Δ = 5000
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:

$\sqrt{\Delta}=\sqrt{5000}=\sqrt{2500*2}=\sqrt{2500}*\sqrt{2}=50\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50\sqrt{2}}{2*25}=\frac{50-50\sqrt{2}}{50}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50\sqrt{2}}{2*25}=\frac{50+50\sqrt{2}}{50}
$