5/6x+1/8x=2

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

5/6x+1/8x=2

We move all terms to the left:

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


40x/48x^2+6x/48x^2-2=0

We multiply all the terms by the denominator


40x+6x-2*48x^2=0

We add all the numbers together, and all the variables

46x-2*48x^2=0

Wy multiply elements

-96x^2+46x=0

a = -96; b = 46; c = 0;
Δ = b2-4ac
Δ = 462-4·(-96)·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-46}{2*-96}=\frac{-92}{-192}
=23/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+46}{2*-96}=\frac{0}{-192}
=0
$