6/x-5+1=2x-4/x-5

Solution for 6/x-5+1=2x-4/x-5 equation:

6/x-5+1=2x-4/x-5

We move all terms to the left:

6/x-5+1-(2x-4/x-5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-5)!=0

x∈R


We add all the numbers together, and all the variables

6/x-(2x-4/x-5)-4=0

We get rid of parentheses

6/x-2x+4/x+5-4=0

We multiply all the terms by the denominator


-2x*x+5*x-4*x+6+4=0

We add all the numbers together, and all the variables

x-2x*x+10=0

Wy multiply elements

-2x^2+x+10=0

a = -2; b = 1; c = +10;
Δ = b2-4ac
Δ = 12-4·(-2)·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*-2}=\frac{8}{-4}
=-2
$