2/5x-7/3x=1

Solution for 2/5x-7/3x=1 equation:

2/5x-7/3x=1

We move all terms to the left:

2/5x-7/3x-(1)=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


6x/15x^2+(-35x)/15x^2-1=0

We multiply all the terms by the denominator


6x+(-35x)-1*15x^2=0

Wy multiply elements

-15x^2+6x+(-35x)=0

We get rid of parentheses

-15x^2+6x-35x=0

We add all the numbers together, and all the variables

-15x^2-29x=0

a = -15; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·(-15)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*-15}=\frac{0}{-30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*-15}=\frac{58}{-30}
=-1+14/15
$