x/3x+4=9x+3

Solution for x/3x+4=9x+3 equation:

x/3x+4=9x+3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-27x^2+x-9x+12x=0

We add all the numbers together, and all the variables

-27x^2+4x=0

a = -27; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-27)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-27}=\frac{-8}{-54}
=4/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-27}=\frac{0}{-54}
=0
$