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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-1x-5=0

a = 1; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·1·(-5)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{21}}{2*1}=\frac{1-\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{21}}{2*1}=\frac{1+\sqrt{21}}{2}
$