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

Solution for (2a-5)(a+8)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2a^2+11a-40=0

a = 2; b = 11; c = -40;
Δ = b2-4ac
Δ = 112-4·2·(-40)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-21}{2*2}=\frac{-32}{4}
=-8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+21}{2*2}=\frac{10}{4}
=2+1/2
$