2x+13/3x=15

Solution for 2x+13/3x=15 equation:

2x+13/3x=15

We move all terms to the left:

2x+13/3x-(15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-15*3x+13=0

Wy multiply elements

6x^2-45x+13=0

a = 6; b = -45; c = +13;
Δ = b2-4ac
Δ = -452-4·6·13
Δ = 1713
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1713}}{2*6}=\frac{45-\sqrt{1713}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1713}}{2*6}=\frac{45+\sqrt{1713}}{12}
$