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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-384x^2)/256x^2+128x/256x^2+(-160x)/256x^2-3=0

We multiply all the terms by the denominator


(-384x^2)+128x+(-160x)-3*256x^2=0

Wy multiply elements

(-384x^2)-768x^2+128x+(-160x)=0

We get rid of parentheses

-384x^2-768x^2+128x-160x=0

We add all the numbers together, and all the variables

-1152x^2-32x=0

a = -1152; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-1152)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-1152}=\frac{0}{-2304}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-1152}=\frac{64}{-2304}
=-1/36
$