6x-6/x-5=0

Solution for 6x-6/x-5=0 equation:

6x-6/x-5=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


6x*x-5*x-6=0

We add all the numbers together, and all the variables

-5x+6x*x-6=0

Wy multiply elements

6x^2-5x-6=0

a = 6; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·6·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*6}=\frac{-8}{12}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*6}=\frac{18}{12}
=1+1/2
$