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

Solution for 1/3x+4-9x+1=0 equation:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-9x+1/3x+5=0

We multiply all the terms by the denominator


-9x*3x+5*3x+1=0

Wy multiply elements

-27x^2+15x+1=0

a = -27; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-27)·1
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{37}}{2*-27}=\frac{-15-3\sqrt{37}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{37}}{2*-27}=\frac{-15+3\sqrt{37}}{-54}
$