3/8x-6=2-1/2x

Solution for 3/8x-6=2-1/2x equation:

3/8x-6=2-1/2x

We move all terms to the left:

3/8x-6-(2-1/2x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/8x-(-1/2x+2)-6=0

We get rid of parentheses

3/8x+1/2x-2-6=0

We calculate fractions


6x/16x^2+8x/16x^2-2-6=0

We add all the numbers together, and all the variables

6x/16x^2+8x/16x^2-8=0

We multiply all the terms by the denominator


6x+8x-8*16x^2=0

We add all the numbers together, and all the variables

14x-8*16x^2=0

Wy multiply elements

-128x^2+14x=0

a = -128; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-128)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-128}=\frac{-28}{-256}
=7/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-128}=\frac{0}{-256}
=0
$