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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-8x)/512x^2+192x/512x^2+24x/512x^2-1=0

We multiply all the terms by the denominator


(-8x)+192x+24x-1*512x^2=0

We add all the numbers together, and all the variables

216x+(-8x)-1*512x^2=0

Wy multiply elements

-512x^2+216x+(-8x)=0

We get rid of parentheses

-512x^2+216x-8x=0

We add all the numbers together, and all the variables

-512x^2+208x=0

a = -512; b = 208; c = 0;
Δ = b2-4ac
Δ = 2082-4·(-512)·0
Δ = 43264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43264}=208$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-208}{2*-512}=\frac{-416}{-1024}
=13/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+208}{2*-512}=\frac{0}{-1024}
=0
$