2x-1/9x=4

Solution for 2x-1/9x=4 equation:

2x-1/9x=4

We move all terms to the left:

2x-1/9x-(4)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


2x*9x-4*9x-1=0

Wy multiply elements

18x^2-36x-1=0

a = 18; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·18·(-1)
Δ = 1368
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:

$\sqrt{\Delta}=\sqrt{1368}=\sqrt{36*38}=\sqrt{36}*\sqrt{38}=6\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{38}}{2*18}=\frac{36-6\sqrt{38}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{38}}{2*18}=\frac{36+6\sqrt{38}}{36}
$