585t=5t^2+20t

Solution for 585t=5t^2+20t equation:

585t=5t^2+20t

We move all terms to the left:

585t-(5t^2+20t)=0

We get rid of parentheses

-5t^2+585t-20t=0

We add all the numbers together, and all the variables

-5t^2+565t=0

a = -5; b = 565; c = 0;
Δ = b2-4ac
Δ = 5652-4·(-5)·0
Δ = 319225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{319225}=565$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(565)-565}{2*-5}=\frac{-1130}{-10}
=+113
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(565)+565}{2*-5}=\frac{0}{-10}
=0
$