-2/3x-1/4x=-11

Solution for -2/3x-1/4x=-11 equation:

-2/3x-1/4x=-11

We move all terms to the left:

-2/3x-1/4x-(-11)=0


Domain of the equation: 3x!=0

x!=0/3

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

-2/3x-1/4x+11=0

We calculate fractions


(-8x)/12x^2+(-3x)/12x^2+11=0

We multiply all the terms by the denominator


(-8x)+(-3x)+11*12x^2=0

Wy multiply elements

132x^2+(-8x)+(-3x)=0

We get rid of parentheses

132x^2-8x-3x=0

We add all the numbers together, and all the variables

132x^2-11x=0

a = 132; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·132·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*132}=\frac{0}{264}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*132}=\frac{22}{264}
=1/12
$