7/8x+3/2=5/4x-3

Solution for 7/8x+3/2=5/4x-3 equation:

7/8x+3/2=5/4x-3

We move all terms to the left:

7/8x+3/2-(5/4x-3)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x-3)!=0

x∈R


We get rid of parentheses

7/8x-5/4x+3+3/2=0

We calculate fractions


384x^2/128x^2+112x/128x^2+(-160x)/128x^2+3=0

We multiply all the terms by the denominator


384x^2+112x+(-160x)+3*128x^2=0

Wy multiply elements

384x^2+384x^2+112x+(-160x)=0

We get rid of parentheses

384x^2+384x^2+112x-160x=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{0}{1536}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*768}=\frac{96}{1536}
=1/16
$