6h^2=414

Solution for 6h^2=414 equation:

6h^2=414

We move all terms to the left:

6h^2-(414)=0

a = 6; b = 0; c = -414;
Δ = b2-4ac
Δ = 02-4·6·(-414)
Δ = 9936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9936}=\sqrt{144*69}=\sqrt{144}*\sqrt{69}=12\sqrt{69}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{69}}{2*6}=\frac{0-12\sqrt{69}}{12}
=-\frac{12\sqrt{69}}{12}
=-\sqrt{69}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{69}}{2*6}=\frac{0+12\sqrt{69}}{12}
=\frac{12\sqrt{69}}{12}
=\sqrt{69}
$