2-16t=6(-3t2)

Solution for 2-16t=6(-3t2) equation:

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

We move all terms to the left:

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


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

6(-3t^2)

We multiply parentheses

-18t^2

Back to the equation:

-(-18t^2)


We get rid of parentheses

18t^2-16t+2=0

a = 18; b = -16; c = +2;
Δ = b2-4ac
Δ = -162-4·18·2
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{7}}{2*18}=\frac{16-4\sqrt{7}}{36}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{7}}{2*18}=\frac{16+4\sqrt{7}}{36}
$