t=5t^2-10t

Solution for t=5t^2-10t equation:

t=5t^2-10t

We move all terms to the left:

t-(5t^2-10t)=0

We get rid of parentheses

-5t^2+t+10t=0

We add all the numbers together, and all the variables

-5t^2+11t=0

a = -5; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-5)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-5}=\frac{-22}{-10}
=2+1/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-5}=\frac{0}{-10}
=0
$