6=x(1+2x)

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

6=x(1+2x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

x(2x+1)

We multiply parentheses

2x^2+x

Back to the equation:

-(2x^2+x)


We get rid of parentheses

-2x^2-x+6=0

We add all the numbers together, and all the variables

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

a = -2; b = -1; c = +6;
Δ = b2-4ac
Δ = -12-4·(-2)·6
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*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*-2}=\frac{8}{-4}
=-2
$