2-16t=(-3t+2)t

Solution for 2-16t=(-3t+2)t equation:

2-16t=(-3t+2)t

We move all terms to the left:

2-16t-((-3t+2)t)=0


We calculate terms in parentheses: -((-3t+2)t), so:

(-3t+2)t

We multiply parentheses

-3t^2+2t

Back to the equation:

-(-3t^2+2t)


We get rid of parentheses

3t^2-2t-16t+2=0

We add all the numbers together, and all the variables

3t^2-18t+2=0

a = 3; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·3·2
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-10\sqrt{3}}{2*3}=\frac{18-10\sqrt{3}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10\sqrt{3}}{2*3}=\frac{18+10\sqrt{3}}{6}
$