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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5x^2-25x+4x+20)-(x+1)(x+5)=0

We get rid of parentheses

-5x^2-25x+4x-(x+1)(x+5)+20=0

We multiply parentheses ..

-5x^2-(+x^2+5x+x+5)-25x+4x+20=0

We add all the numbers together, and all the variables

-5x^2-(+x^2+5x+x+5)-21x+20=0

We get rid of parentheses

-5x^2-x^2-5x-x-21x-5+20=0

We add all the numbers together, and all the variables

-6x^2-27x+15=0

a = -6; b = -27; c = +15;
Δ = b2-4ac
Δ = -272-4·(-6)·15
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-33}{2*-6}=\frac{-6}{-12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+33}{2*-6}=\frac{60}{-12}
=-5
$