t=-2t(t-14)

Solution for t=-2t(t-14) equation:

t=-2t(t-14)

We move all terms to the left:

t-(-2t(t-14))=0


We calculate terms in parentheses: -(-2t(t-14)), so:

-2t(t-14)

We multiply parentheses

-2t^2+28t

Back to the equation:

-(-2t^2+28t)


We get rid of parentheses

2t^2-28t+t=0

We add all the numbers together, and all the variables

2t^2-27t=0

a = 2; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·2·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*2}=\frac{0}{4}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*2}=\frac{54}{4}
=13+1/2
$