3/5x+1/3x=42

Solution for 3/5x+1/3x=42 equation:

3/5x+1/3x=42

We move all terms to the left:

3/5x+1/3x-(42)=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+5x/15x^2-42=0

We multiply all the terms by the denominator


9x+5x-42*15x^2=0

We add all the numbers together, and all the variables

14x-42*15x^2=0

Wy multiply elements

-630x^2+14x=0

a = -630; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-630)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-630}=\frac{-28}{-1260}
=1/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-630}=\frac{0}{-1260}
=0
$