3a+(2a+5)+2a(a+2)=13

Solution for 3a+(2a+5)+2a(a+2)=13 equation:

3a+(2a+5)+2a(a+2)=13

We move all terms to the left:

3a+(2a+5)+2a(a+2)-(13)=0

We multiply parentheses

2a^2+3a+(2a+5)+4a-13=0

We get rid of parentheses

2a^2+3a+2a+4a+5-13=0

We add all the numbers together, and all the variables

2a^2+9a-8=0

a = 2; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·2·(-8)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{145}}{2*2}=\frac{-9-\sqrt{145}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{145}}{2*2}=\frac{-9+\sqrt{145}}{4}
$