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

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

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

We multiply parentheses ..

(+4x^2+16x-10x-40)=0

We get rid of parentheses

4x^2+16x-10x-40=0

We add all the numbers together, and all the variables

4x^2+6x-40=0

a = 4; b = 6; c = -40;
Δ = b2-4ac
Δ = 62-4·4·(-40)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-26}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+26}{2*4}=\frac{20}{8}
=2+1/2
$