11/6x+1+11/4x=14/3

Solution for 11/6x+1+11/4x=14/3 equation:

11/6x+1+11/4x=14/3

We move all terms to the left:

11/6x+1+11/4x-(14/3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

11/6x+11/4x+1-(+14/3)=0

We get rid of parentheses

11/6x+11/4x+1-14/3=0

We calculate fractions


(-1344x^2)/216x^2+396x/216x^2+594x/216x^2+1=0

We multiply all the terms by the denominator


(-1344x^2)+396x+594x+1*216x^2=0

We add all the numbers together, and all the variables

(-1344x^2)+990x+1*216x^2=0

Wy multiply elements

(-1344x^2)+216x^2+990x=0

We get rid of parentheses

-1344x^2+216x^2+990x=0

We add all the numbers together, and all the variables

-1128x^2+990x=0

a = -1128; b = 990; c = 0;
Δ = b2-4ac
Δ = 9902-4·(-1128)·0
Δ = 980100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{980100}=990$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(990)-990}{2*-1128}=\frac{-1980}{-2256}
=165/188
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(990)+990}{2*-1128}=\frac{0}{-2256}
=0
$