(x+5)(x-1)=21

Solution for (x+5)(x-1)=21 equation:

(x+5)(x-1)=21

We move all terms to the left:

(x+5)(x-1)-(21)=0

We multiply parentheses ..

(+x^2-1x+5x-5)-21=0

We get rid of parentheses

x^2-1x+5x-5-21=0

We add all the numbers together, and all the variables

x^2+4x-26=0

a = 1; b = 4; c = -26;
Δ = b2-4ac
Δ = 42-4·1·(-26)
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{30}}{2*1}=\frac{-4-2\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{30}}{2*1}=\frac{-4+2\sqrt{30}}{2}
$