-3/4x+6-1/6x=8

Solution for -3/4x+6-1/6x=8 equation:

-3/4x+6-1/6x=8

We move all terms to the left:

-3/4x+6-1/6x-(8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-3/4x-1/6x-2=0

We calculate fractions


(-18x)/24x^2+(-4x)/24x^2-2=0

We multiply all the terms by the denominator


(-18x)+(-4x)-2*24x^2=0

Wy multiply elements

-48x^2+(-18x)+(-4x)=0

We get rid of parentheses

-48x^2-18x-4x=0

We add all the numbers together, and all the variables

-48x^2-22x=0

a = -48; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-48)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-48}=\frac{44}{-96}
=-11/24
$