3/(x+1)+6x=5

Solution for 3/(x+1)+6x=5 equation:

3/(x+1)+6x=5

We move all terms to the left:

3/(x+1)+6x-(5)=0


Domain of the equation: (x+1)!=0

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

x!=-1

x∈R


We add all the numbers together, and all the variables

6x+3/(x+1)-5=0

We multiply all the terms by the denominator


6x*(x+1)-5*(x+1)+3=0

We multiply parentheses

6x^2+6x-5x-5+3=0

We add all the numbers together, and all the variables

6x^2+x-2=0

a = 6; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·6·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*6}=\frac{-8}{12}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*6}=\frac{6}{12}
=1/2
$