6z2-9=0

Solution for 6z2-9=0 equation:

6z^2-9=0

a = 6; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·6·(-9)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*6}=\frac{0-6\sqrt{6}}{12}
=-\frac{6\sqrt{6}}{12}
=-\frac{\sqrt{6}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*6}=\frac{0+6\sqrt{6}}{12}
=\frac{6\sqrt{6}}{12}
=\frac{\sqrt{6}}{2}
$