5x-13/3x+3=0

Solution for 5x-13/3x+3=0 equation:

5x-13/3x+3=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


5x*3x+3*3x-13=0

Wy multiply elements

15x^2+9x-13=0

a = 15; b = 9; c = -13;
Δ = b2-4ac
Δ = 92-4·15·(-13)
Δ = 861
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{-(9)-\sqrt{861}}{2*15}=\frac{-9-\sqrt{861}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{861}}{2*15}=\frac{-9+\sqrt{861}}{30}
$