4/9(x-1)=28/9-(x-7x)+1

Solution for 4/9(x-1)=28/9-(x-7x)+1 equation:

4/9(x-1)=28/9-(x-7x)+1

We move all terms to the left:

4/9(x-1)-(28/9-(x-7x)+1)=0


Domain of the equation: 9(x-1)!=0

x∈R



Domain of the equation: 9-(x-7x)+1)!=0

We move all terms containing x to the left, all other terms to the right

-(x-7x)+1)!=-9

x∈R


We add all the numbers together, and all the variables

4/9(x-1)-(28/9-(-6x)+1)=0

We calculate fractions


6x/(87x-81)+(-252xx/(87x-81)=0


We calculate terms in parentheses: +(-252xx/(87x-81), so:

-252xx/(87x-81

We multiply all the terms by the denominator


-252xx

Back to the equation:

+(-252xx)


We get rid of parentheses

6x/(87x-81)-252xx=0

We multiply all the terms by the denominator


6x-252xx*(87x-81)=0

We multiply parentheses

-21924x^2+6x+20412x=0

We add all the numbers together, and all the variables

-21924x^2+20418x=0

a = -21924; b = 20418; c = 0;
Δ = b2-4ac
Δ = 204182-4·(-21924)·0
Δ = 416894724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{416894724}=20418$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20418)-20418}{2*-21924}=\frac{-40836}{-43848}
=3403/3654
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20418)+20418}{2*-21924}=\frac{0}{-43848}
=0
$