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-(-8x+7)/9x-(4x+3)-(2.3)=0

We add all the numbers together, and all the variables

x-(-8x+7)/9x-(4x+3)-2.3=0

We get rid of parentheses

x-(-8x+7)/9x-4x-3-2.3=0

We multiply all the terms by the denominator


x*9x-(-8x+7)-4x*9x-3*9x-(2.3)*9x=0

We multiply parentheses

x*9x-(-8x+7)-4x*9x-3*9x-20.7x=0

Wy multiply elements

9x^2-36x^2-(-8x+7)-27x-20.7x=0

We get rid of parentheses

9x^2-36x^2+8x-27x-20.7x-7=0

We add all the numbers together, and all the variables

-27x^2-39.7x-7=0

a = -27; b = -39.7; c = -7;
Δ = b2-4ac
Δ = -39.72-4·(-27)·(-7)
Δ = 820.09
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39.7)-\sqrt{820.09}}{2*-27}=\frac{39.7-\sqrt{820.09}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39.7)+\sqrt{820.09}}{2*-27}=\frac{39.7+\sqrt{820.09}}{-54}
$