3/4x+1/6x=11

Solution for 3/4x+1/6x=11 equation:

3/4x+1/6x=11

We move all terms to the left:

3/4x+1/6x-(11)=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 calculate fractions


18x/24x^2+4x/24x^2-11=0

We multiply all the terms by the denominator


18x+4x-11*24x^2=0

We add all the numbers together, and all the variables

22x-11*24x^2=0

Wy multiply elements

-264x^2+22x=0

a = -264; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-264)·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*-264}=\frac{-44}{-528}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-264}=\frac{0}{-528}
=0
$