(2a-5)(a+8)=a

Solution for (2a-5)(a+8)=a equation:

(2a-5)(a+8)=a

We move all terms to the left:

(2a-5)(a+8)-(a)=0

We add all the numbers together, and all the variables

-1a+(2a-5)(a+8)=0

We multiply parentheses ..

(+2a^2+16a-5a-40)-1a=0

We get rid of parentheses

2a^2+16a-5a-1a-40=0

We add all the numbers together, and all the variables

2a^2+10a-40=0

a = 2; b = 10; c = -40;
Δ = b2-4ac
Δ = 102-4·2·(-40)
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{105}}{2*2}=\frac{-10-2\sqrt{105}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{105}}{2*2}=\frac{-10+2\sqrt{105}}{4}
$