5/2*x-7/4=3/8*x

Solution for 5/2*x-7/4=3/8*x equation:

5/2x-7/4=3/8x

We move all terms to the left:

5/2x-7/4-(3/8x)=0


Domain of the equation: 2x!=0

x!=0/2

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

5/2x-(+3/8x)-7/4=0

We get rid of parentheses

5/2x-3/8x-7/4=0

We calculate fractions


(-896x^2)/256x^2+640x/256x^2+(-96x)/256x^2=0

We multiply all the terms by the denominator


(-896x^2)+640x+(-96x)=0

We get rid of parentheses

-896x^2+640x-96x=0

We add all the numbers together, and all the variables

-896x^2+544x=0

a = -896; b = 544; c = 0;
Δ = b2-4ac
Δ = 5442-4·(-896)·0
Δ = 295936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{295936}=544$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(544)-544}{2*-896}=\frac{-1088}{-1792}
=17/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(544)+544}{2*-896}=\frac{0}{-1792}
=0
$