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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

9x^2-3x+12x+1=0

We add all the numbers together, and all the variables

9x^2+9x+1=0

a = 9; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·9·1
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{5}}{2*9}=\frac{-9-3\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{5}}{2*9}=\frac{-9+3\sqrt{5}}{18}
$