3/5x+5/3x=50

Solution for 3/5x+5/3x=50 equation:

3/5x+5/3x=50

We move all terms to the left:

3/5x+5/3x-(50)=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


9x/15x^2+25x/15x^2-50=0

We multiply all the terms by the denominator


9x+25x-50*15x^2=0

We add all the numbers together, and all the variables

34x-50*15x^2=0

Wy multiply elements

-750x^2+34x=0

a = -750; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-750)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-750}=\frac{-68}{-1500}
=17/375
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-750}=\frac{0}{-1500}
=0
$