2/3x-2/5x=7

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

2/3x-2/5x=7

We move all terms to the left:

2/3x-2/5x-(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 calculate fractions


10x/15x^2+(-6x)/15x^2-7=0

We multiply all the terms by the denominator


10x+(-6x)-7*15x^2=0

Wy multiply elements

-105x^2+10x+(-6x)=0

We get rid of parentheses

-105x^2+10x-6x=0

We add all the numbers together, and all the variables

-105x^2+4x=0

a = -105; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-105)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-105}=\frac{-8}{-210}
=4/105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-105}=\frac{0}{-210}
=0
$