6z^2=450

Solution for 6z^2=450 equation:

6z^2=450

We move all terms to the left:

6z^2-(450)=0

a = 6; b = 0; c = -450;
Δ = b2-4ac
Δ = 02-4·6·(-450)
Δ = 10800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{3}}{2*6}=\frac{0-60\sqrt{3}}{12}
=-\frac{60\sqrt{3}}{12}
=-5\sqrt{3}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{3}}{2*6}=\frac{0+60\sqrt{3}}{12}
=\frac{60\sqrt{3}}{12}
=5\sqrt{3}
$