1/2x-3/4=328-5/8x

Solution for 1/2x-3/4=328-5/8x equation:

1/2x-3/4=328-5/8x

We move all terms to the left:

1/2x-3/4-(328-5/8x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-5/8x+328)-3/4=0

We get rid of parentheses

1/2x+5/8x-328-3/4=0

We calculate fractions


(-384x^2)/256x^2+128x/256x^2+160x/256x^2-328=0

We multiply all the terms by the denominator


(-384x^2)+128x+160x-328*256x^2=0

We add all the numbers together, and all the variables

(-384x^2)+288x-328*256x^2=0

Wy multiply elements

(-384x^2)-83968x^2+288x=0

We get rid of parentheses

-384x^2-83968x^2+288x=0

We add all the numbers together, and all the variables

-84352x^2+288x=0

a = -84352; b = 288; c = 0;
Δ = b2-4ac
Δ = 2882-4·(-84352)·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-288}{2*-84352}=\frac{-576}{-168704}
=9/2636
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+288}{2*-84352}=\frac{0}{-168704}
=0
$