12/3x+23/5x=64

Solution for 12/3x+23/5x=64 equation:

12/3x+23/5x=64

We move all terms to the left:

12/3x+23/5x-(64)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


60x/15x^2+69x/15x^2-64=0

We multiply all the terms by the denominator


60x+69x-64*15x^2=0

We add all the numbers together, and all the variables

129x-64*15x^2=0

Wy multiply elements

-960x^2+129x=0

a = -960; b = 129; c = 0;
Δ = b2-4ac
Δ = 1292-4·(-960)·0
Δ = 16641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16641}=129$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(129)-129}{2*-960}=\frac{-258}{-1920}
=43/320
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(129)+129}{2*-960}=\frac{0}{-1920}
=0
$