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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-256x^2)/128x^2+96x/128x^2+(-48x)/128x^2-4=0

We multiply all the terms by the denominator


(-256x^2)+96x+(-48x)-4*128x^2=0

Wy multiply elements

(-256x^2)-512x^2+96x+(-48x)=0

We get rid of parentheses

-256x^2-512x^2+96x-48x=0

We add all the numbers together, and all the variables

-768x^2+48x=0

a = -768; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·(-768)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*-768}=\frac{-96}{-1536}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*-768}=\frac{0}{-1536}
=0
$