13/2x+2/3x=47

Solution for 13/2x+2/3x=47 equation:

13/2x+2/3x=47

We move all terms to the left:

13/2x+2/3x-(47)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


39x/6x^2+4x/6x^2-47=0

We multiply all the terms by the denominator


39x+4x-47*6x^2=0

We add all the numbers together, and all the variables

43x-47*6x^2=0

Wy multiply elements

-282x^2+43x=0

a = -282; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·(-282)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*-282}=\frac{-86}{-564}
=43/282
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*-282}=\frac{0}{-564}
=0
$