3/4x-1/2=5/8x+2

Solution for 3/4x-1/2=5/8x+2 equation:

3/4x-1/2=5/8x+2

We move all terms to the left:

3/4x-1/2-(5/8x+2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+2)!=0

x∈R


We get rid of parentheses

3/4x-5/8x-2-1/2=0

We calculate fractions


(-256x^2)/128x^2+96x/128x^2+(-80x)/128x^2-2=0

We multiply all the terms by the denominator


(-256x^2)+96x+(-80x)-2*128x^2=0

Wy multiply elements

(-256x^2)-256x^2+96x+(-80x)=0

We get rid of parentheses

-256x^2-256x^2+96x-80x=0

We add all the numbers together, and all the variables

-512x^2+16x=0

a = -512; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-512)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-512}=\frac{-32}{-1024}
=1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-512}=\frac{0}{-1024}
=0
$