2*x+(x+4)/(x-1)=14

Solution for 2*x+(x+4)/(x-1)=14 equation:

2x+(x+4)/(x-1)=14

We move all terms to the left:

2x+(x+4)/(x-1)-(14)=0


Domain of the equation: (x-1)!=0

We move all terms containing x to the left, all other terms to the right

x!=1

x∈R


We multiply all the terms by the denominator


2x*(x-1)+(x+4)-14*(x-1)=0

We multiply parentheses

2x^2-2x+(x+4)-14x+14=0

We get rid of parentheses

2x^2-2x+x-14x+4+14=0

We add all the numbers together, and all the variables

2x^2-15x+18=0

a = 2; b = -15; c = +18;
Δ = b2-4ac
Δ = -152-4·2·18
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{-(-15)-9}{2*2}=\frac{6}{4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*2}=\frac{24}{4}
=6
$