A=(5z+6)(9z-2)

Solution for A=(5z+6)(9z-2) equation:

=(5A+6)(9A-2)

We move all terms to the left:

-((5A+6)(9A-2))=0

We multiply parentheses ..

-((+45A^2-10A+54A-12))=0


We calculate terms in parentheses: -((+45A^2-10A+54A-12)), so:

(+45A^2-10A+54A-12)

We get rid of parentheses

45A^2-10A+54A-12

We add all the numbers together, and all the variables

45A^2+44A-12

Back to the equation:

-(45A^2+44A-12)


We get rid of parentheses

-45A^2-44A+12=0

a = -45; b = -44; c = +12;
Δ = b2-4ac
Δ = -442-4·(-45)·12
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-64}{2*-45}=\frac{-20}{-90}
=2/9
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+64}{2*-45}=\frac{108}{-90}
=-1+1/5
$