x-7(-8x)/9x-(3+4x)=2/3

Solution for x-7(-8x)/9x-(3+4x)=2/3 equation:

x-7(-8x)/9x-(3+4x)=2/3

We move all terms to the left:

x-7(-8x)/9x-(3+4x)-(2/3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

x-7(-8x)/9x-(4x+3)-(+2/3)=0

We get rid of parentheses

x-7(-8x)/9x-4x-3-2/3=0

We calculate fractions


x-4x+168x/27x+(-18x)/27x-3=0

We add all the numbers together, and all the variables

-3x+168x/27x+(-18x)/27x-3=0

We multiply all the terms by the denominator


-3x*27x+168x+(-18x)-3*27x=0

We add all the numbers together, and all the variables

168x-3x*27x+(-18x)-3*27x=0

Wy multiply elements

-81x^2+168x+(-18x)-81x=0

We get rid of parentheses

-81x^2+168x-18x-81x=0

We add all the numbers together, and all the variables

-81x^2+69x=0

a = -81; b = 69; c = 0;
Δ = b2-4ac
Δ = 692-4·(-81)·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-69}{2*-81}=\frac{-138}{-162}
=23/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+69}{2*-81}=\frac{0}{-162}
=0
$