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

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

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

We multiply parentheses ..

(+5x^2-1x+25x-5)=0

We get rid of parentheses

5x^2-1x+25x-5=0

We add all the numbers together, and all the variables

5x^2+24x-5=0

a = 5; b = 24; c = -5;
Δ = b2-4ac
Δ = 242-4·5·(-5)
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{-(24)-26}{2*5}=\frac{-50}{10}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+26}{2*5}=\frac{2}{10}
=1/5
$