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

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

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

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-384x^2)/128x^2+48x/128x^2+224x/128x^2-5=0

We multiply all the terms by the denominator


(-384x^2)+48x+224x-5*128x^2=0

We add all the numbers together, and all the variables

(-384x^2)+272x-5*128x^2=0

Wy multiply elements

(-384x^2)-640x^2+272x=0

We get rid of parentheses

-384x^2-640x^2+272x=0

We add all the numbers together, and all the variables

-1024x^2+272x=0

a = -1024; b = 272; c = 0;
Δ = b2-4ac
Δ = 2722-4·(-1024)·0
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(272)-272}{2*-1024}=\frac{-544}{-2048}
=17/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(272)+272}{2*-1024}=\frac{0}{-2048}
=0
$