9z^2+12z=1

Solution for 9z^2+12z=1 equation:

9z^2+12z=1

We move all terms to the left:

9z^2+12z-(1)=0

a = 9; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·9·(-1)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{5}}{2*9}=\frac{-12-6\sqrt{5}}{18}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{5}}{2*9}=\frac{-12+6\sqrt{5}}{18}
$