t=-13t^2+572t

Solution for t=-13t^2+572t equation:

t=-13t^2+572t

We move all terms to the left:

t-(-13t^2+572t)=0

We get rid of parentheses

13t^2-572t+t=0

We add all the numbers together, and all the variables

13t^2-571t=0

a = 13; b = -571; c = 0;
Δ = b2-4ac
Δ = -5712-4·13·0
Δ = 326041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{326041}=571$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-571)-571}{2*13}=\frac{0}{26}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-571)+571}{2*13}=\frac{1142}{26}
=43+12/13
$