57=2t+6t^2

Solution for 57=2t+6t^2 equation:

57=2t+6t^2

We move all terms to the left:

57-(2t+6t^2)=0

We get rid of parentheses

-6t^2-2t+57=0

a = -6; b = -2; c = +57;
Δ = b2-4ac
Δ = -22-4·(-6)·57
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14\sqrt{7}}{2*-6}=\frac{2-14\sqrt{7}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14\sqrt{7}}{2*-6}=\frac{2+14\sqrt{7}}{-12}
$