7x-6/x-18=1

Solution for 7x-6/x-18=1 equation:

7x-6/x-18=1

We move all terms to the left:

7x-6/x-18-(1)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7x-6/x-19=0

We multiply all the terms by the denominator


7x*x-19*x-6=0

We add all the numbers together, and all the variables

-19x+7x*x-6=0

Wy multiply elements

7x^2-19x-6=0

a = 7; b = -19; c = -6;
Δ = b2-4ac
Δ = -192-4·7·(-6)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-23}{2*7}=\frac{-4}{14}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+23}{2*7}=\frac{42}{14}
=3
$