(3x-1)(x+3)/x+6=0

Solution for (3x-1)(x+3)/x+6=0 equation:

(3x-1)(x+3)/x+6=0


Domain of the equation: x!=0

x∈R


We multiply parentheses ..

(+3x^2+9x-1x-3)/x+6=0

We multiply all the terms by the denominator


(+3x^2+9x-1x-3)+6*x=0

We add all the numbers together, and all the variables

(+3x^2+9x-1x-3)+6x=0

We get rid of parentheses

3x^2+9x-1x+6x-3=0

We add all the numbers together, and all the variables

3x^2+14x-3=0

a = 3; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·3·(-3)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{58}}{2*3}=\frac{-14-2\sqrt{58}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{58}}{2*3}=\frac{-14+2\sqrt{58}}{6}
$