0=t^2-850t+2500

Solution for 0=t^2-850t+2500 equation:

0=t^2-850t+2500

We move all terms to the left:

0-(t^2-850t+2500)=0

We add all the numbers together, and all the variables

-(t^2-850t+2500)=0

We get rid of parentheses

-t^2+850t-2500=0

We add all the numbers together, and all the variables

-1t^2+850t-2500=0

a = -1; b = 850; c = -2500;
Δ = b2-4ac
Δ = 8502-4·(-1)·(-2500)
Δ = 712500
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:

$\sqrt{\Delta}=\sqrt{712500}=\sqrt{2500*285}=\sqrt{2500}*\sqrt{285}=50\sqrt{285}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(850)-50\sqrt{285}}{2*-1}=\frac{-850-50\sqrt{285}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(850)+50\sqrt{285}}{2*-1}=\frac{-850+50\sqrt{285}}{-2}
$