2a-21=39/a+1

Solution for 2a-21=39/a+1 equation:

2a-21=39/a+1

We move all terms to the left:

2a-21-(39/a+1)=0


Domain of the equation: a+1)!=0

a∈R


We get rid of parentheses

2a-39/a-1-21=0

We multiply all the terms by the denominator


2a*a-1*a-21*a-39=0

We add all the numbers together, and all the variables

-22a+2a*a-39=0

Wy multiply elements

2a^2-22a-39=0

a = 2; b = -22; c = -39;
Δ = b2-4ac
Δ = -222-4·2·(-39)
Δ = 796
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{199}}{2*2}=\frac{22-2\sqrt{199}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{199}}{2*2}=\frac{22+2\sqrt{199}}{4}
$