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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

a^2-3a-2=0

a = 1; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·1·(-2)
Δ = 17
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{17}}{2*1}=\frac{3-\sqrt{17}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{17}}{2*1}=\frac{3+\sqrt{17}}{2}
$