(x+5)(4x-1)=0

Solution for (x+5)(4x-1)=0 equation:

(x+5)(4x-1)=0

We multiply parentheses ..

(+4x^2-1x+20x-5)=0

We get rid of parentheses

4x^2-1x+20x-5=0

We add all the numbers together, and all the variables

4x^2+19x-5=0

a = 4; b = 19; c = -5;
Δ = b2-4ac
Δ = 192-4·4·(-5)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-21}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+21}{2*4}=\frac{2}{8}
=1/4
$