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

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

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

We move all terms to the left:

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


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

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

a!=1

a∈R


We multiply all the terms by the denominator


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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2a^2-15a+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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*2}=\frac{6}{4}
=1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*2}=\frac{24}{4}
=6
$