9z2-18z=1

Solution for 9z2-18z=1 equation:

9z^2-18z=1

We move all terms to the left:

9z^2-18z-(1)=0

a = 9; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·9·(-1)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{10}}{2*9}=\frac{18-6\sqrt{10}}{18}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{10}}{2*9}=\frac{18+6\sqrt{10}}{18}
$