7/9*x=x-126

Solution for 7/9*x=x-126 equation:

7/9x=x-126

We move all terms to the left:

7/9x-(x-126)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

7/9x-x+126=0

We multiply all the terms by the denominator


-x*9x+126*9x+7=0

Wy multiply elements

-9x^2+1134x+7=0

a = -9; b = 1134; c = +7;
Δ = b2-4ac
Δ = 11342-4·(-9)·7
Δ = 1286208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1286208}=\sqrt{576*2233}=\sqrt{576}*\sqrt{2233}=24\sqrt{2233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1134)-24\sqrt{2233}}{2*-9}=\frac{-1134-24\sqrt{2233}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1134)+24\sqrt{2233}}{2*-9}=\frac{-1134+24\sqrt{2233}}{-18}
$