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

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

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

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


-3x-8x+12x/27x+(-36x)/27x+7+2=0

We add all the numbers together, and all the variables

-11x+12x/27x+(-36x)/27x+9=0

We multiply all the terms by the denominator


-11x*27x+12x+(-36x)+9*27x=0

We add all the numbers together, and all the variables

12x-11x*27x+(-36x)+9*27x=0

Wy multiply elements

-297x^2+12x+(-36x)+243x=0

We get rid of parentheses

-297x^2+12x-36x+243x=0

We add all the numbers together, and all the variables

-297x^2+219x=0

a = -297; b = 219; c = 0;
Δ = b2-4ac
Δ = 2192-4·(-297)·0
Δ = 47961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{47961}=219$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(219)-219}{2*-297}=\frac{-438}{-594}
=73/99
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(219)+219}{2*-297}=\frac{0}{-594}
=0
$