-9z+9=4z^2

Solution for -9z+9=4z^2 equation:

-9z+9=4z^2

We move all terms to the left:

-9z+9-(4z^2)=0

determiningTheFunctionDomain
-4z^2-9z+9=0

a = -4; b = -9; c = +9;
Δ = b2-4ac
Δ = -92-4·(-4)·9
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*-4}=\frac{-6}{-8}
=3/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*-4}=\frac{24}{-8}
=-3
$