6^1=x^2/(x+1)

Solution for 6^1=x^2/(x+1) equation:

6^1=x^2/(x+1)

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: -(x^2+6*(x+1)), so:

x^2+6*(x+1)

We multiply parentheses

x^2+6x+6

Back to the equation:

-(x^2+6x+6)


We get rid of parentheses

-x^2-6x-6=0

We add all the numbers together, and all the variables

-1x^2-6x-6=0

a = -1; b = -6; c = -6;
Δ = b2-4ac
Δ = -62-4·(-1)·(-6)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*-1}=\frac{6-2\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*-1}=\frac{6+2\sqrt{3}}{-2}
$