25-t^2=10t

Solution for 25-t^2=10t equation:

25-t^2=10t

We move all terms to the left:

25-t^2-(10t)=0

We add all the numbers together, and all the variables

-1t^2-10t+25=0

a = -1; b = -10; c = +25;
Δ = b2-4ac
Δ = -102-4·(-1)·25
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{2}}{2*-1}=\frac{10-10\sqrt{2}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{2}}{2*-1}=\frac{10+10\sqrt{2}}{-2}
$