(x-1)(x+5)=2x+4x-2

Solution for (x-1)(x+5)=2x+4x-2 equation:

(x-1)(x+5)=2x+4x-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

(x-1)(x+5)-(6x-2)=0

We get rid of parentheses

(x-1)(x+5)-6x+2=0

We multiply parentheses ..

(+x^2+5x-1x-5)-6x+2=0

We get rid of parentheses

x^2+5x-1x-6x-5+2=0

We add all the numbers together, and all the variables

x^2-2x-3=0

a = 1; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·1·(-3)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*1}=\frac{6}{2}
=3
$