4-7/9x=x+2

Solution for 4-7/9x=x+2 equation:

4-7/9x=x+2

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-x*9x-2*9x+4*9x-7=0

Wy multiply elements

-9x^2-18x+36x-7=0

We add all the numbers together, and all the variables

-9x^2+18x-7=0

a = -9; b = 18; c = -7;
Δ = b2-4ac
Δ = 182-4·(-9)·(-7)
Δ = 72
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:

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