x(1+2x)=66

Solution for x(1+2x)=66 equation:

x(1+2x)=66

We move all terms to the left:

x(1+2x)-(66)=0

We add all the numbers together, and all the variables

x(2x+1)-66=0

We multiply parentheses

2x^2+x-66=0

a = 2; b = 1; c = -66;
Δ = b2-4ac
Δ = 12-4·2·(-66)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-23}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+23}{2*2}=\frac{22}{4}
=5+1/2
$