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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


192x/128x^2+(-2x)/128x^2+(-14x)/128x^2-2=0

We multiply all the terms by the denominator


192x+(-2x)+(-14x)-2*128x^2=0

Wy multiply elements

-256x^2+192x+(-2x)+(-14x)=0

We get rid of parentheses

-256x^2+192x-2x-14x=0

We add all the numbers together, and all the variables

-256x^2+176x=0

a = -256; b = 176; c = 0;
Δ = b2-4ac
Δ = 1762-4·(-256)·0
Δ = 30976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{30976}=176$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-176}{2*-256}=\frac{-352}{-512}
=11/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+176}{2*-256}=\frac{0}{-512}
=0
$