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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+x^2-5x+2x-10)-1=0

We get rid of parentheses

x^2-5x+2x-10-1=0

We add all the numbers together, and all the variables

x^2-3x-11=0

a = 1; b = -3; c = -11;
Δ = b2-4ac
Δ = -32-4·1·(-11)
Δ = 53
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{53}}{2*1}=\frac{3-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{53}}{2*1}=\frac{3+\sqrt{53}}{2}
$