2/3x-4=2/5x-7

Solution for 2/3x-4=2/5x-7 equation:

2/3x-4=2/5x-7

We move all terms to the left:

2/3x-4-(2/5x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x-7)!=0

x∈R


We get rid of parentheses

2/3x-2/5x+7-4=0

We calculate fractions


10x/15x^2+(-6x)/15x^2+7-4=0

We add all the numbers together, and all the variables

10x/15x^2+(-6x)/15x^2+3=0

We multiply all the terms by the denominator


10x+(-6x)+3*15x^2=0

Wy multiply elements

45x^2+10x+(-6x)=0

We get rid of parentheses

45x^2+10x-6x=0

We add all the numbers together, and all the variables

45x^2+4x=0

a = 45; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·45·0
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*45}=\frac{-8}{90}
=-4/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*45}=\frac{0}{90}
=0
$