X(x-9)/2x-9=6

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Solution for X(x-9)/2x-9=6 equation:



X(X-9)/2X-9=6
We move all terms to the left:
X(X-9)/2X-9-(6)=0
Domain of the equation: 2X!=0
X!=0/2
X!=0
X∈R
We add all the numbers together, and all the variables
X(X-9)/2X-15=0
We multiply all the terms by the denominator
X(X-9)-15*2X=0
We multiply parentheses
X^2-9X-15*2X=0
Wy multiply elements
X^2-9X-30X=0
We add all the numbers together, and all the variables
X^2-39X=0
a = 1; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·1·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*1}=\frac{0}{2} =0 $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*1}=\frac{78}{2} =39 $

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