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

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
$