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

Solution for a(2a+5)+2(2a+5)=0 equation:

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

We multiply parentheses

2a^2+5a+4a+10=0

We add all the numbers together, and all the variables

2a^2+9a+10=0

a = 2; b = 9; c = +10;
Δ = b2-4ac
Δ = 92-4·2·10
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*2}=\frac{-10}{4}
=-2+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*2}=\frac{-8}{4}
=-2
$