4a+1/3a=13

Solution for 4a+1/3a=13 equation:

4a+1/3a=13

We move all terms to the left:

4a+1/3a-(13)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We multiply all the terms by the denominator


4a*3a-13*3a+1=0

Wy multiply elements

12a^2-39a+1=0

a = 12; b = -39; c = +1;
Δ = b2-4ac
Δ = -392-4·12·1
Δ = 1473
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1473}}{2*12}=\frac{39-\sqrt{1473}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1473}}{2*12}=\frac{39+\sqrt{1473}}{24}
$