6/3=a+5/a+12

Solution for 6/3=a+5/a+12 equation:

6/3=a+5/a+12

We move all terms to the left:

6/3-(a+5/a+12)=0


Domain of the equation: a+12)!=0

a∈R


We add all the numbers together, and all the variables

-(a+5/a+12)+2=0

We get rid of parentheses

-a-5/a-12+2=0

We multiply all the terms by the denominator


-a*a-12*a+2*a-5=0

We add all the numbers together, and all the variables

-10a-a*a-5=0

Wy multiply elements

-1a^2-10a-5=0

a = -1; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·(-1)·(-5)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{5}}{2*-1}=\frac{10-4\sqrt{5}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{5}}{2*-1}=\frac{10+4\sqrt{5}}{-2}
$