0=100t-5(t*t)

Solution for 0=100t-5(t*t) equation:

0=100t-5(t*t)

We move all terms to the left:

0-(100t-5(t*t))=0

We add all the numbers together, and all the variables

-(100t-5(+t*t))+0=0

We add all the numbers together, and all the variables

-(100t-5(+t*t))=0


We calculate terms in parentheses: -(100t-5(+t*t)), so:

100t-5(+t*t)

We multiply parentheses

-5t^2+100t

Back to the equation:

-(-5t^2+100t)


We get rid of parentheses

5t^2-100t=0

a = 5; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·5·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*5}=\frac{0}{10}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*5}=\frac{200}{10}
=20
$