55=(a)(2a+1)

Solution for 55=(a)(2a+1) equation:

55=(a)(2a+1)

We move all terms to the left:

55-((a)(2a+1))=0


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

a(2a+1)

We multiply parentheses

2a^2+a

Back to the equation:

-(2a^2+a)


We get rid of parentheses

-2a^2-a+55=0

We add all the numbers together, and all the variables

-2a^2-1a+55=0

a = -2; b = -1; c = +55;
Δ = b2-4ac
Δ = -12-4·(-2)·55
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-21}{2*-2}=\frac{-20}{-4}
=+5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+21}{2*-2}=\frac{22}{-4}
=-5+1/2
$