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

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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} $

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