20t(t-5)=5t

Solution for 20t(t-5)=5t equation:

20t(t-5)=5t

We move all terms to the left:

20t(t-5)-(5t)=0

We add all the numbers together, and all the variables

-5t+20t(t-5)=0

We multiply parentheses

20t^2-5t-100t=0

We add all the numbers together, and all the variables

20t^2-105t=0

a = 20; b = -105; c = 0;
Δ = b2-4ac
Δ = -1052-4·20·0
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11025}=105$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-105}{2*20}=\frac{0}{40}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+105}{2*20}=\frac{210}{40}
=5+1/4
$