a(a+1)=2.6-2a

Solution for a(a+1)=2.6-2a equation:

a(a+1)=2.6-2a

We move all terms to the left:

a(a+1)-(2.6-2a)=0

We add all the numbers together, and all the variables

a(a+1)-(-2a+2.6)=0

We multiply parentheses

a^2+a-(-2a+2.6)=0

We get rid of parentheses

a^2+a+2a-2.6=0

We add all the numbers together, and all the variables

a^2+3a-2.6=0

a = 1; b = 3; c = -2.6;
Δ = b2-4ac
Δ = 32-4·1·(-2.6)
Δ = 19.4
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{-(3)-\sqrt{19.4}}{2*1}=\frac{-3-\sqrt{19.4}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{19.4}}{2*1}=\frac{-3+\sqrt{19.4}}{2}
$