13/5x+12/3x=24

Solution for 13/5x+12/3x=24 equation:

13/5x+12/3x=24

We move all terms to the left:

13/5x+12/3x-(24)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


39x/15x^2+60x/15x^2-24=0

We multiply all the terms by the denominator


39x+60x-24*15x^2=0

We add all the numbers together, and all the variables

99x-24*15x^2=0

Wy multiply elements

-360x^2+99x=0

a = -360; b = 99; c = 0;
Δ = b2-4ac
Δ = 992-4·(-360)·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(99)-99}{2*-360}=\frac{-198}{-720}
=11/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(99)+99}{2*-360}=\frac{0}{-720}
=0
$