2/3x+1/5x=3/7

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

2/3x+1/5x=3/7

We move all terms to the left:

2/3x+1/5x-(3/7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+1/5x-(+3/7)=0

We get rid of parentheses

2/3x+1/5x-3/7=0

We calculate fractions


(-225x^2)/735x^2+490x/735x^2+147x/735x^2=0

We multiply all the terms by the denominator


(-225x^2)+490x+147x=0

We add all the numbers together, and all the variables

(-225x^2)+637x=0

We get rid of parentheses

-225x^2+637x=0

a = -225; b = 637; c = 0;
Δ = b2-4ac
Δ = 6372-4·(-225)·0
Δ = 405769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{405769}=637$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(637)-637}{2*-225}=\frac{-1274}{-450}
=2+187/225
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(637)+637}{2*-225}=\frac{0}{-450}
=0
$