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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


(-100x^2)/90x^2+225x/90x^2+(-126x)/90x^2=0

We multiply all the terms by the denominator


(-100x^2)+225x+(-126x)=0

We get rid of parentheses

-100x^2+225x-126x=0

We add all the numbers together, and all the variables

-100x^2+99x=0

a = -100; b = 99; c = 0;
Δ = b2-4ac
Δ = 992-4·(-100)·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(99)-99}{2*-100}=\frac{-198}{-200}
=99/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(99)+99}{2*-100}=\frac{0}{-200}
=0
$