9x=1/3x-4

Solution for 9x=1/3x-4 equation:

9x=1/3x-4

We move all terms to the left:

9x-(1/3x-4)=0


Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

9x-1/3x+4=0

We multiply all the terms by the denominator


9x*3x+4*3x-1=0

Wy multiply elements

27x^2+12x-1=0

a = 27; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·27·(-1)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{7}}{2*27}=\frac{-12-6\sqrt{7}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{7}}{2*27}=\frac{-12+6\sqrt{7}}{54}
$