2x-1/9x=-28

Solution for 2x-1/9x=-28 equation:

2x-1/9x=-28

We move all terms to the left:

2x-1/9x-(-28)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

2x-1/9x+28=0

We multiply all the terms by the denominator


2x*9x+28*9x-1=0

Wy multiply elements

18x^2+252x-1=0

a = 18; b = 252; c = -1;
Δ = b2-4ac
Δ = 2522-4·18·(-1)
Δ = 63576
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:

$\sqrt{\Delta}=\sqrt{63576}=\sqrt{36*1766}=\sqrt{36}*\sqrt{1766}=6\sqrt{1766}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-6\sqrt{1766}}{2*18}=\frac{-252-6\sqrt{1766}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+6\sqrt{1766}}{2*18}=\frac{-252+6\sqrt{1766}}{36}
$