6/5x+7/3x=30

Solution for 6/5x+7/3x=30 equation:

6/5x+7/3x=30

We move all terms to the left:

6/5x+7/3x-(30)=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


18x/15x^2+35x/15x^2-30=0

We multiply all the terms by the denominator


18x+35x-30*15x^2=0

We add all the numbers together, and all the variables

53x-30*15x^2=0

Wy multiply elements

-450x^2+53x=0

a = -450; b = 53; c = 0;
Δ = b2-4ac
Δ = 532-4·(-450)·0
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-53}{2*-450}=\frac{-106}{-900}
=53/450
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+53}{2*-450}=\frac{0}{-900}
=0
$