66=x(2x-1)

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

66=x(2x-1)

We move all terms to the left:

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


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

x(2x-1)

We multiply parentheses

2x^2-1x

Back to the equation:

-(2x^2-1x)


We get rid of parentheses

-2x^2+1x+66=0

We add all the numbers together, and all the variables

-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
$