66=(2x+1)x

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

66=(2x+1)x

We move all terms to the left:

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


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

(2x+1)x

We multiply parentheses

2x^2+x

Back to the equation:

-(2x^2+x)


We get rid of parentheses

-2x^2-x+66=0

We add all the numbers together, and all the variables

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