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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


160x^2/512x^2+256x/512x^2+(-384x)/512x^2+2=0

We multiply all the terms by the denominator


160x^2+256x+(-384x)+2*512x^2=0

Wy multiply elements

160x^2+1024x^2+256x+(-384x)=0

We get rid of parentheses

160x^2+1024x^2+256x-384x=0

We add all the numbers together, and all the variables

1184x^2-128x=0

a = 1184; b = -128; c = 0;
Δ = b2-4ac
Δ = -1282-4·1184·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-128}{2*1184}=\frac{0}{2368}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+128}{2*1184}=\frac{256}{2368}
=4/37
$