(x+7)(x-2)=1

Solution for (x+7)(x-2)=1 equation:

(x+7)(x-2)=1

We move all terms to the left:

(x+7)(x-2)-(1)=0

We multiply parentheses ..

(+x^2-2x+7x-14)-1=0

We get rid of parentheses

x^2-2x+7x-14-1=0

We add all the numbers together, and all the variables

x^2+5x-15=0

a = 1; b = 5; c = -15;
Δ = b2-4ac
Δ = 52-4·1·(-15)
Δ = 85
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{-(5)-\sqrt{85}}{2*1}=\frac{-5-\sqrt{85}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{85}}{2*1}=\frac{-5+\sqrt{85}}{2}
$