5/9x-x=-32

Solution for 5/9x-x=-32 equation:

5/9x-x=-32

We move all terms to the left:

5/9x-x-(-32)=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+5/9x+32=0

We multiply all the terms by the denominator


-1x*9x+32*9x+5=0

Wy multiply elements

-9x^2+288x+5=0

a = -9; b = 288; c = +5;
Δ = b2-4ac
Δ = 2882-4·(-9)·5
Δ = 83124
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:

$\sqrt{\Delta}=\sqrt{83124}=\sqrt{36*2309}=\sqrt{36}*\sqrt{2309}=6\sqrt{2309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(288)-6\sqrt{2309}}{2*-9}=\frac{-288-6\sqrt{2309}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(288)+6\sqrt{2309}}{2*-9}=\frac{-288+6\sqrt{2309}}{-18}
$