9x-(x-18)=2x(9+x)

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Solution for 9x-(x-18)=2x(9+x) equation:



9x-(x-18)=2x(9+x)
We move all terms to the left:
9x-(x-18)-(2x(9+x))=0
We add all the numbers together, and all the variables
9x-(x-18)-(2x(x+9))=0
We get rid of parentheses
9x-x-(2x(x+9))+18=0
We calculate terms in parentheses: -(2x(x+9)), so:
2x(x+9)
We multiply parentheses
2x^2+18x
Back to the equation:
-(2x^2+18x)
We add all the numbers together, and all the variables
8x-(2x^2+18x)+18=0
We get rid of parentheses
-2x^2+8x-18x+18=0
We add all the numbers together, and all the variables
-2x^2-10x+18=0
a = -2; b = -10; c = +18;
Δ = b2-4ac
Δ = -102-4·(-2)·18
Δ = 244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{61}}{2*-2}=\frac{10-2\sqrt{61}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{61}}{2*-2}=\frac{10+2\sqrt{61}}{-4} $

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