1/6x+1/8x=1

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

1/6x+1/8x=1

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


8x/48x^2+6x/48x^2-1=0

We multiply all the terms by the denominator


8x+6x-1*48x^2=0

We add all the numbers together, and all the variables

14x-1*48x^2=0

Wy multiply elements

-48x^2+14x=0

a = -48; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-48)·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*-48}=\frac{-28}{-96}
=7/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-48}=\frac{0}{-96}
=0
$