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

Solution for (-5x-1)(2x+8)=0 equation:

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

We multiply parentheses ..

(-10x^2-40x-2x-8)=0

We get rid of parentheses

-10x^2-40x-2x-8=0

We add all the numbers together, and all the variables

-10x^2-42x-8=0

a = -10; b = -42; c = -8;
Δ = b2-4ac
Δ = -422-4·(-10)·(-8)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-38}{2*-10}=\frac{4}{-20}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+38}{2*-10}=\frac{80}{-20}
=-4
$