3/4x+1/8=7/16x+2

Solution for 3/4x+1/8=7/16x+2 equation:

3/4x+1/8=7/16x+2

We move all terms to the left:

3/4x+1/8-(7/16x+2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 16x+2)!=0

x∈R


We get rid of parentheses

3/4x-7/16x-2+1/8=0

We calculate fractions


64x^2/4096x^2+3072x/4096x^2+(-1792x)/4096x^2-2=0

We multiply all the terms by the denominator


64x^2+3072x+(-1792x)-2*4096x^2=0

Wy multiply elements

64x^2-8192x^2+3072x+(-1792x)=0

We get rid of parentheses

64x^2-8192x^2+3072x-1792x=0

We add all the numbers together, and all the variables

-8128x^2+1280x=0

a = -8128; b = 1280; c = 0;
Δ = b2-4ac
Δ = 12802-4·(-8128)·0
Δ = 1638400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1638400}=1280$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1280)-1280}{2*-8128}=\frac{-2560}{-16256}
=20/127
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1280)+1280}{2*-8128}=\frac{0}{-16256}
=0
$