1/9x+4=2x

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

1/9x+4=2x

We move all terms to the left:

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

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}
$