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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

384x^2+512x^2+128x+(-160x)=0

We get rid of parentheses

384x^2+512x^2+128x-160x=0

We add all the numbers together, and all the variables

896x^2-32x=0

a = 896; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·896·0
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*896}=\frac{0}{1792}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*896}=\frac{64}{1792}
=1/28
$