3x+(5/x-6)=2x

Solution for 3x+(5/x-6)=2x equation:

3x+(5/x-6)=2x

We move all terms to the left:

3x+(5/x-6)-(2x)=0


Domain of the equation: x-6)!=0

x∈R


We add all the numbers together, and all the variables

x+(5/x-6)=0

We get rid of parentheses

x+5/x-6=0

We multiply all the terms by the denominator


x*x-6*x+5=0

We add all the numbers together, and all the variables

-6x+x*x+5=0

Wy multiply elements

x^2-6x+5=0

a = 1; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*1}=\frac{10}{2}
=5
$