3/a=a-6

Solution for 3/a=a-6 equation:

3/a=a-6

We move all terms to the left:

3/a-(a-6)=0


Domain of the equation: a!=0

a∈R


We get rid of parentheses

3/a-a+6=0

We multiply all the terms by the denominator


-a*a+6*a+3=0

We add all the numbers together, and all the variables

6a-a*a+3=0

Wy multiply elements

-1a^2+6a+3=0

a = -1; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-1)·3
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{3}}{2*-1}=\frac{-6-4\sqrt{3}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{3}}{2*-1}=\frac{-6+4\sqrt{3}}{-2}
$