1/2x+3/8=5/4x

Solution for 1/2x+3/8=5/4x equation:

1/2x+3/8=5/4x

We move all terms to the left:

1/2x+3/8-(5/4x)=0


Domain of the equation: 2x!=0

x!=0/2

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

1/2x-(+5/4x)+3/8=0

We get rid of parentheses

1/2x-5/4x+3/8=0

We calculate fractions


96x^2/512x^2+256x/512x^2+(-640x)/512x^2=0

We multiply all the terms by the denominator


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

We get rid of parentheses

96x^2+256x-640x=0

We add all the numbers together, and all the variables

96x^2-384x=0

a = 96; b = -384; c = 0;
Δ = b2-4ac
Δ = -3842-4·96·0
Δ = 147456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{147456}=384$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-384)-384}{2*96}=\frac{0}{192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-384)+384}{2*96}=\frac{768}{192}
=4
$