4/9x+6=x-4

Solution for 4/9x+6=x-4 equation:

4/9x+6=x-4

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

4/9x-x+4+6=0

We multiply all the terms by the denominator


-x*9x+4*9x+6*9x+4=0

Wy multiply elements

-9x^2+36x+54x+4=0

We add all the numbers together, and all the variables

-9x^2+90x+4=0

a = -9; b = 90; c = +4;
Δ = b2-4ac
Δ = 902-4·(-9)·4
Δ = 8244
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:

$\sqrt{\Delta}=\sqrt{8244}=\sqrt{36*229}=\sqrt{36}*\sqrt{229}=6\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{229}}{2*-9}=\frac{-90-6\sqrt{229}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{229}}{2*-9}=\frac{-90+6\sqrt{229}}{-18}
$