z=9z^2-9z-10

Solution for z=9z^2-9z-10 equation:

z=9z^2-9z-10

We move all terms to the left:

z-(9z^2-9z-10)=0

We get rid of parentheses

-9z^2+z+9z+10=0

We add all the numbers together, and all the variables

-9z^2+10z+10=0

a = -9; b = 10; c = +10;
Δ = b2-4ac
Δ = 102-4·(-9)·10
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{115}}{2*-9}=\frac{-10-2\sqrt{115}}{-18}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{115}}{2*-9}=\frac{-10+2\sqrt{115}}{-18}
$