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

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

(X-1)(X+4)=1

We move all terms to the left:

(X-1)(X+4)-(1)=0

We multiply parentheses ..

(+X^2+4X-1X-4)-1=0

We get rid of parentheses

X^2+4X-1X-4-1=0

We add all the numbers together, and all the variables

X^2+3X-5=0

a = 1; b = 3; c = -5;
Δ = b2-4ac
Δ = 32-4·1·(-5)
Δ = 29
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{-(3)-\sqrt{29}}{2*1}=\frac{-3-\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{29}}{2*1}=\frac{-3+\sqrt{29}}{2}
$