5/4x-9/5=3/8x

Solution for 5/4x-9/5=3/8x equation:

5/4x-9/5=3/8x

We move all terms to the left:

5/4x-9/5-(3/8x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-(+3/8x)-9/5=0

We get rid of parentheses

5/4x-3/8x-9/5=0

We calculate fractions


(-2304x^2)/800x^2+1000x/800x^2+(-300x)/800x^2=0

We multiply all the terms by the denominator


(-2304x^2)+1000x+(-300x)=0

We get rid of parentheses

-2304x^2+1000x-300x=0

We add all the numbers together, and all the variables

-2304x^2+700x=0

a = -2304; b = 700; c = 0;
Δ = b2-4ac
Δ = 7002-4·(-2304)·0
Δ = 490000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{490000}=700$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-700}{2*-2304}=\frac{-1400}{-4608}
=175/576
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+700}{2*-2304}=\frac{0}{-4608}
=0
$