x-3/3x+1=-3

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

x-3/3x+1=-3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x-3/3x+4=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+12x-3=0

a = 3; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·3·(-3)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{5}}{2*3}=\frac{-12-6\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{5}}{2*3}=\frac{-12+6\sqrt{5}}{6}
$