a(a+5)=-2(a+5)

Solution for a(a+5)=-2(a+5) equation:

a(a+5)=-2(a+5)

We move all terms to the left:

a(a+5)-(-2(a+5))=0

We multiply parentheses

a^2+5a-(-2(a+5))=0


We calculate terms in parentheses: -(-2(a+5)), so:

-2(a+5)

We multiply parentheses

-2a-10

Back to the equation:

-(-2a-10)


We get rid of parentheses

a^2+5a+2a+10=0

We add all the numbers together, and all the variables

a^2+7a+10=0

a = 1; b = 7; c = +10;
Δ = b2-4ac
Δ = 72-4·1·10
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*1}=\frac{-10}{2}
=-5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*1}=\frac{-4}{2}
=-2
$