13x*3^x=39

Solution for 13x*3^x=39 equation:

13x*3^x=39

We move all terms to the left:

13x*3^x-(39)=0

Wy multiply elements

39x^2-39=0

a = 39; b = 0; c = -39;
Δ = b2-4ac
Δ = 02-4·39·(-39)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-78}{2*39}=\frac{-78}{78}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+78}{2*39}=\frac{78}{78}
=1
$