3x-9/6x-18=1

Solution for 3x-9/6x-18=1 equation:

3x-9/6x-18=1

We move all terms to the left:

3x-9/6x-18-(1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3x-9/6x-19=0

We multiply all the terms by the denominator


3x*6x-19*6x-9=0

Wy multiply elements

18x^2-114x-9=0

a = 18; b = -114; c = -9;
Δ = b2-4ac
Δ = -1142-4·18·(-9)
Δ = 13644
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:

$\sqrt{\Delta}=\sqrt{13644}=\sqrt{36*379}=\sqrt{36}*\sqrt{379}=6\sqrt{379}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-6\sqrt{379}}{2*18}=\frac{114-6\sqrt{379}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+6\sqrt{379}}{2*18}=\frac{114+6\sqrt{379}}{36}
$