7/9x-8=x

Solution for 7/9x-8=x equation:

7/9x-8=x

We move all terms to the left:

7/9x-8-(x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/9x-8=0

We multiply all the terms by the denominator


-1x*9x-8*9x+7=0

Wy multiply elements

-9x^2-72x+7=0

a = -9; b = -72; c = +7;
Δ = b2-4ac
Δ = -722-4·(-9)·7
Δ = 5436
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:

$\sqrt{\Delta}=\sqrt{5436}=\sqrt{36*151}=\sqrt{36}*\sqrt{151}=6\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{151}}{2*-9}=\frac{72-6\sqrt{151}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{151}}{2*-9}=\frac{72+6\sqrt{151}}{-18}
$