x(x+11)=-2(x+21)

Solution for x(x+11)=-2(x+21) equation:

x(x+11)=-2(x+21)

We move all terms to the left:

x(x+11)-(-2(x+21))=0

We multiply parentheses

x^2+11x-(-2(x+21))=0


We calculate terms in parentheses: -(-2(x+21)), so:

-2(x+21)

We multiply parentheses

-2x-42

Back to the equation:

-(-2x-42)


We get rid of parentheses

x^2+11x+2x+42=0

We add all the numbers together, and all the variables

x^2+13x+42=0

a = 1; b = 13; c = +42;
Δ = b2-4ac
Δ = 132-4·1·42
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-1}{2*1}=\frac{-14}{2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+1}{2*1}=\frac{-12}{2}
=-6
$