2/3x-11=4+4/7x

Solution for 2/3x-11=4+4/7x equation:

2/3x-11=4+4/7x

We move all terms to the left:

2/3x-11-(4+4/7x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(4/7x+4)-11=0

We get rid of parentheses

2/3x-4/7x-4-11=0

We calculate fractions


14x/21x^2+(-12x)/21x^2-4-11=0

We add all the numbers together, and all the variables

14x/21x^2+(-12x)/21x^2-15=0

We multiply all the terms by the denominator


14x+(-12x)-15*21x^2=0

Wy multiply elements

-315x^2+14x+(-12x)=0

We get rid of parentheses

-315x^2+14x-12x=0

We add all the numbers together, and all the variables

-315x^2+2x=0

a = -315; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-315)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-315}=\frac{-4}{-630}
=2/315
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-315}=\frac{0}{-630}
=0
$