21=(2x+1)(x)

Solution for 21=(2x+1)(x) equation:

21=(2x+1)(x)

We move all terms to the left:

21-((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+21=0

We add all the numbers together, and all the variables

-2x^2-1x+21=0

a = -2; b = -1; c = +21;
Δ = b2-4ac
Δ = -12-4·(-2)·21
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*-2}=\frac{14}{-4}
=-3+1/2
$