7/4x-8/3x=11

Solution for 7/4x-8/3x=11 equation:

7/4x-8/3x=11

We move all terms to the left:

7/4x-8/3x-(11)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


21x/12x^2+(-32x)/12x^2-11=0

We multiply all the terms by the denominator


21x+(-32x)-11*12x^2=0

Wy multiply elements

-132x^2+21x+(-32x)=0

We get rid of parentheses

-132x^2+21x-32x=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
$