1/8x+5-1/2=-8+1/6x

Solution for 1/8x+5-1/2=-8+1/6x equation:

1/8x+5-1/2=-8+1/6x

We move all terms to the left:

1/8x+5-1/2-(-8+1/6x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/8x-(1/6x-8)+5-1/2=0

We get rid of parentheses

1/8x-1/6x+8+5-1/2=0

We calculate fractions


(-288x^2)/192x^2+24x/192x^2+(-32x)/192x^2+8+5=0

We add all the numbers together, and all the variables

(-288x^2)/192x^2+24x/192x^2+(-32x)/192x^2+13=0

We multiply all the terms by the denominator


(-288x^2)+24x+(-32x)+13*192x^2=0

Wy multiply elements

(-288x^2)+2496x^2+24x+(-32x)=0

We get rid of parentheses

-288x^2+2496x^2+24x-32x=0

We add all the numbers together, and all the variables

2208x^2-8x=0

a = 2208; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·2208·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*2208}=\frac{0}{4416}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*2208}=\frac{16}{4416}
=1/276
$