1/8x+14=1/6x

Solution for 1/8x+14=1/6x equation:

1/8x+14=1/6x

We move all terms to the left:

1/8x+14-(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)+14=0

We get rid of parentheses

1/8x-1/6x+14=0

We calculate fractions


6x/48x^2+(-8x)/48x^2+14=0

We multiply all the terms by the denominator


6x+(-8x)+14*48x^2=0

Wy multiply elements

672x^2+6x+(-8x)=0

We get rid of parentheses

672x^2+6x-8x=0

We add all the numbers together, and all the variables

672x^2-2x=0

a = 672; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·672·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*672}=\frac{0}{1344}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*672}=\frac{4}{1344}
=1/336
$