18z^2-30+8=0

Solution for 18z^2-30+8=0 equation:

18z^2-30+8=0

We add all the numbers together, and all the variables

18z^2-22=0

a = 18; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·18·(-22)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{11}}{2*18}=\frac{0-12\sqrt{11}}{36}
=-\frac{12\sqrt{11}}{36}
=-\frac{\sqrt{11}}{3}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{11}}{2*18}=\frac{0+12\sqrt{11}}{36}
=\frac{12\sqrt{11}}{36}
=\frac{\sqrt{11}}{3}
$