16=2(t-1)t

Solution for 16=2(t-1)t equation:

16=2(t-1)t

We move all terms to the left:

16-(2(t-1)t)=0


We calculate terms in parentheses: -(2(t-1)t), so:

2(t-1)t

We multiply parentheses

2t^2-2t

Back to the equation:

-(2t^2-2t)


We get rid of parentheses

-2t^2+2t+16=0

a = -2; b = 2; c = +16;
Δ = b2-4ac
Δ = 22-4·(-2)·16
Δ = 132
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{33}}{2*-2}=\frac{-2-2\sqrt{33}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{33}}{2*-2}=\frac{-2+2\sqrt{33}}{-4}
$