36=(b+9)(b+2)

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Solution for 36=(b+9)(b+2) equation:



36=(b+9)(b+2)
We move all terms to the left:
36-((b+9)(b+2))=0
We multiply parentheses ..
-((+b^2+2b+9b+18))+36=0
We calculate terms in parentheses: -((+b^2+2b+9b+18)), so:
(+b^2+2b+9b+18)
We get rid of parentheses
b^2+2b+9b+18
We add all the numbers together, and all the variables
b^2+11b+18
Back to the equation:
-(b^2+11b+18)
We get rid of parentheses
-b^2-11b-18+36=0
We add all the numbers together, and all the variables
-1b^2-11b+18=0
a = -1; b = -11; c = +18;
Δ = b2-4ac
Δ = -112-4·(-1)·18
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{193}}{2*-1}=\frac{11-\sqrt{193}}{-2} $
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{193}}{2*-1}=\frac{11+\sqrt{193}}{-2} $

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