2-16t=6(-3t+2)t=

Solution for 2-16t=6(-3t+2)t= equation:

2-16t=6(-3t+2)t=

We move all terms to the left:

2-16t-(6(-3t+2)t)=0


We calculate terms in parentheses: -(6(-3t+2)t), so:

6(-3t+2)t

We multiply parentheses

-18t^2+12t

Back to the equation:

-(-18t^2+12t)


We get rid of parentheses

18t^2-12t-16t+2=0

We add all the numbers together, and all the variables

18t^2-28t+2=0

a = 18; b = -28; c = +2;
Δ = b2-4ac
Δ = -282-4·18·2
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8\sqrt{10}}{2*18}=\frac{28-8\sqrt{10}}{36}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8\sqrt{10}}{2*18}=\frac{28+8\sqrt{10}}{36}
$