3/4x-1/2x=7/8

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

3/4x-1/2x=7/8

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-112x^2)/512x^2+384x/512x^2+(-256x)/512x^2=0

We multiply all the terms by the denominator


(-112x^2)+384x+(-256x)=0

We get rid of parentheses

-112x^2+384x-256x=0

We add all the numbers together, and all the variables

-112x^2+128x=0

a = -112; b = 128; c = 0;
Δ = b2-4ac
Δ = 1282-4·(-112)·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128}{2*-112}=\frac{-256}{-224}
=1+1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*-112}=\frac{0}{-224}
=0
$