2a+3/a=6

Solution for 2a+3/a=6 equation:

2a+3/a=6

We move all terms to the left:

2a+3/a-(6)=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


2a*a-6*a+3=0

We add all the numbers together, and all the variables

-6a+2a*a+3=0

Wy multiply elements

2a^2-6a+3=0

a = 2; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·2·3
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*2}=\frac{6-2\sqrt{3}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*2}=\frac{6+2\sqrt{3}}{4}
$