6/(x+7)=3x

Solution for 6/(x+7)=3x equation:

6/(x+7)=3x

We move all terms to the left:

6/(x+7)-(3x)=0


Domain of the equation: (x+7)!=0

We move all terms containing x to the left, all other terms to the right

x!=-7

x∈R


We add all the numbers together, and all the variables

-3x+6/(x+7)=0

We multiply all the terms by the denominator


-3x*(x+7)+6=0

We multiply parentheses

-3x^2-21x+6=0

a = -3; b = -21; c = +6;
Δ = b2-4ac
Δ = -212-4·(-3)·6
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{57}}{2*-3}=\frac{21-3\sqrt{57}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{57}}{2*-3}=\frac{21+3\sqrt{57}}{-6}
$