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

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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 $

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