6t^2=18

Solution for 6t^2=18 equation:

6t^2=18

We move all terms to the left:

6t^2-(18)=0

a = 6; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·6·(-18)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*6}=\frac{0-12\sqrt{3}}{12}
=-\frac{12\sqrt{3}}{12}
=-\sqrt{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*6}=\frac{0+12\sqrt{3}}{12}
=\frac{12\sqrt{3}}{12}
=\sqrt{3}
$