9x-27/2x-6=0

Solution for 9x-27/2x-6=0 equation:

9x-27/2x-6=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


9x*2x-6*2x-27=0

Wy multiply elements

18x^2-12x-27=0

a = 18; b = -12; c = -27;
Δ = b2-4ac
Δ = -122-4·18·(-27)
Δ = 2088
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:

$\sqrt{\Delta}=\sqrt{2088}=\sqrt{36*58}=\sqrt{36}*\sqrt{58}=6\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{58}}{2*18}=\frac{12-6\sqrt{58}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{58}}{2*18}=\frac{12+6\sqrt{58}}{36}
$